What are two numbers that add to 25 and divide to 4

Students from Westridge School for Girls in the USA, Cedric from Australian International School Malaysia, Poppy and Gracie from Walton High School in England, students from Humanitree in Mexico, Florence from Walthamstow Hall Junior School in the UK, Eric and Lucia from Willowbank School in New Zealand, Abdullah from Poland, students from Frederick Irwin Anglican School in Australia, John from Poolesville ES in the USA, Bracha and Antoine from St Philip's CofE Primary School Cambridge in the UK, Park from Renaissance International School Sigon in Korea, Diya from the UK, Deniz from North Leamington School in the UK, Ira from Coldspring3 and Adi from the New Beacon in the UK all described how the computer works out your starting number.
Kristin from Westridge School for Girls sent this explanation: All you have to do is do the problem backwards. For example, if your number is 1 then you add 4, double that, subtract 7, and you will get 3. All the computer has to do is do the problem backwards. 3$+$7 (opposite of $-$7) is 10. 10$\div$2 (opposite of $\times$2) is 5. $-$4 (opposite of $+$4) is 1, which was my original number.

Inhaltsverzeichnis Show

What are the product and sum of 6 and 8?
What are the product and sum of 9 and 3?
What are the product and sum of -7 and 9?
Write down two numbers that have a product of 42.
What are the product and sum of 2, 4 and 9?
Questions & Answers

Luigi from Humanitree and Karrthic from Australian International School Malaysia found an algebraic expression for the final number. This is Karrthic's work:

The operation is $(x +4) \times 2 -7= y$ For example $(5 + 4) = 9\\ 9 \times2 = 18\\ 18-7=11$ When you reverse the operation, you find $x$

Furkan from TED Ankara Koleji in Turkey, Bernd and Qianwei from Humanitree and Shriya from International School Frankfurt in Germany showed what the computer does algebraically. This is Qianwei's work:

$(x+4) \times 2 - 7=y$ If we want to get $x$, we need to do the opposite of this equation. Start with $y.$ In the equation $7$ [was subtracted], so we need to add $7$ to $y$ $(7+y)$ In the equation, $(x+4)$ was doubled, we need to divide it by two to get the opposite. $(7+y)\div2$ In the equation, $x$ was added [to] $4$, to get the opposite, we need to take away $4$ from $x.$ $(y+7)\div2-4$ Finally the equation we used to find $x$ will be: $(y+7)\div2-4=x$

Furkan and Shriya simplified the equation before 'reversing' it. This is Furkan's work:

$(x+4) \times2 - 7$ is equal to $2x + 1,$ so we subtract $1$ from the result and divide by $2$ to get the starting number.

Alex from Humanitree and Fernando from Academia Britanica Cuscatleca in El Salvador noticed a different pattern in the numbers from the computer. This is Fernando's work:

When following the instructions given in the problem, if [you give the computer random integers as the result of your calculation], you will get random numbers.

However, when we start with 1 and try until five, you will notice the sequence:

Number you tell the computer was your answer	Number the computer says you started from
1	0
2	0.5
3	1
4	1.5
5	2

As you can see, the sequence is progressing by 0.5, thus is linear. It is adding 0.5 so, and we can see that when 0.5$\times n$ is done, you the sequence now looks like this:

Number you tell the computer was your answer ($n$)	Number the computer says you started from	0.5$\times n$
1	0	0.5
2	0.5	1
3	1	1.5
4	1.5	2
5	2	2.5

The answer to the subsitution is always 0.5 greater than the actual answer, therefore, we need to always substract 0.5 Therefore, the instructions are directly 0.5$n-$0.5 !

Can you see how this result is related to Furkan's equation?

We received lots of sets of instructions for similar activities.
These instructions are from Tamara from Humanitree:

.Think of a number .multiply it by 4 .subtract 2 .add 1 Your number was”¦ So if the final number was 19 first you would need to subtract 1. That would equal to 18. Then you would need to add 2, which would equal to 20. And [finally] you would need to divide it by 4. This equals to 5 so the first number would be 5.

Federico from Humanitree used algebra:

Subtract 10 Divide by 4 Add 5 If the number was $n$ You would do $(n-5) \times4 +10 = $ end number ($x$) Then the computer would do this operation to get the original value of $n:$ $(x-10)\div4 +5 =$ starting number This operation would give you the original results.

Abdullah from Poland wrote a Python program to guess your number:

print("YOUR NUMBER WAS...") print() print("Press [ENTER] after you made each move.") print() input("Think of a number.") print() input("Add 9") print() input("Divide it by 4") print() input("Subtract 6") print() input("Triple it") print() input("Subtract 23") number = float(input("Now, type in number you finished with and then press enter.")) print("Processing...") answer = (((number + 23) / 3) + 6) * 4 - 9 print("You chose the number %s" % answer)

Leila C and Scarlett K from Westridge School for Girls and KSc from Cheadle Academy sent in interesting sets of instructions which will always give the same result, like in the problem Your Number Is... If you follow these instructions, will it ever be possible for the computer to work out what number you started from?

These are KSc's instructions:

Think of a number: $x$ $\lt\lt\lt$ [Input] number
Add $3$: $x+3$
Double it: $2x+6$ $\lt\lt\lt$ Begin to balance out dividable equation
Add $4$: $2x+10$ $\lt\lt\lt$ Equation can now be easily divided
Divide by $2$: $x+5$ $\lt\lt\lt$ Simplify equation
Subtract [original] number from [current] number: $x+5\hspace{2mm}-x$ $\lt\lt\lt$ Balace equation [balancing $x$ with $-x$]
$x=$ always $5$ $\lt\lt\lt x$ is always fixed at $5$

Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.

Read on for an easy explanation of these concepts, along with helpful examples.

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If you are asked to work out the product of two or more numbers, then you need to multiply the numbers together. If you are asked to find the sum of two or more numbers, then you need to add the numbers together.

Below, we will work through several examples together.

In a Nutshell

"Product" means multiply.

"Sum" means add.

What are the product and sum of 6 and 8?

The product of 6 and 8 is 6 × 8 = 48
The sum of 6 and 8 is 6 + 8 = 14

What are the product and sum of 9 and 3?

Work out the product and sum of 9 and 3.

The product of 9 and 3 is 9 × 3 = 27
The sum of 9 and 3 is 9 + 3 = 12

What are the product and sum of -7 and 9?

The product of -7 and 9 is -7 × 9 = -63
The sum of -7 and 9 is -7 + 9 = 2

Write down two numbers that have a product of 42.

All you need to do is look for two numbers that multiply to give 42. There are several possible answers:

1 and 42
2 and 21
3 and 14
6 and 7
-1 and -42
-2 and -21
-3 and -14
-6 and -7

What are the product and sum of 2, 4 and 9?

Work out the product of 2, 4 and 9.

The product means that you need to multiply the three numbers together.

2 × 4 × 9 = 72

The sum means that you need to add the three numbers together.

2 + 4 + 9 = 15

Questions & Answers

Question: What do you get if you double 15?

Answer: Just multiply the number by 2 to give 30.

Question: Can you find two numbers which have a product of 12 and a sum of 7?

Answer: 4 and 3 are a the answers.

4 multiplied by 3 is 12. 4 add 3 is 7.

Question: How do you multiply the sum of 12 and 8 by their difference?

Answer: The sum of 12 and 8 is 12 add 8 which is 20.

The difference between 12 and 8 is 12 minus 8 which is 4.

Now 20 times 4 is 80.

Question: what is the sum and product of -5 and -12?

Answer: Sum means you need to add the numbers (-5 + -12 = -5 - 12 = -17).

Product means you need to multiply the numbers (-5 multiplied by -12 = 60).

Question: What is the product of 5/9×15?

Answer: Write 15 as a fraction as 15/1, now multiply the fraction together to give 25/3.

Question: What is the sum of 1/9, 2/3, and 5/18?

Answer: Just add all of the 3 fractions up by converting them to 18 on the denominator:

2/18 + 12/18 + 5/18 = 19/18.

Question: The product of 4/3 and a number is 84. What is the number?

Answer: Divide 84 by 4/3 to give 63.

Question: What is the product of 27 and 45?

Answer: To work out the product multiply the numbers together, so 27 times 45 is 1215.

Question: Can you find two numbers which have a product of 8 and a sum of -9?

Answer: The two numbers are -1 and -8, since -1 added to -8 is -9, and -1 times -8 os 8.

Question: What is the sum of 84 and 32 doubled?

Answer: To find the sum of 84 and 32 add these numbers together to give 116.

Now to double 116, multiply the number by 2 to give 232.

Question: Can you write a mathematical equation for the following; the sum of two numbers is 3 more than the product?

Answer: x + y + 3 = xy

Question: What is the product of 5,6,and 2?

Answer: 5 times 6 is 30, and 30 times 2 is 60.

Just multiply the numbers together when working out a product.

Question: Work out the sum of 8 /15 and 4 /15 ?

Answer: To find the sum of the two fractions add the fractions together.

The answer will be 12/15, or 4/5 when simplified.

Question: What is the sum of −8+(−2)?

Answer: The answer is -10.

Question: The quotient of two numbers is 1. Their sum is 6. What are the two numbers?

Answer: The two numbers are both 3, since 3 divided by 3 is 1, and 3 added to 3 is 6.

Question: When the product of 6 and 6 is divided by the sum of 6 and 6, what is the quotient?

Answer: The product of 6 and 6 is 6 times 6 which is 36.

The sum of 6 and 6 is 6 add 6 which is 12.

The quotient of 36 and 12 is 36 divided by 12 which is 3.

Question: Two numbers have a sum of 1 and a product of −20. What are the numbers?

Answer: The two numbers are -4 and 5, since -4 added to 5 is 1, and -4 times 5 is -20.

Question: How does one solve this problem: Multiply the sum of 83 and 74 by their difference, and divide the product by 15?

Answer: The sum of 83 and 74 is 157 (add them together).

The difference between 83 and 74 is 9 (take them away).

Now multiply 157 by 9 to give 1413.

Now divide 1413 by 15 to give 94.2.

Question: Can you find two numbers that have the sum of 35 and a difference of 15?

Answer: The two numbers that solve this problem are 25 and 10.

This is becuase 25 + 10 gives 35 (sum means add), and 25 - 10 gives 15 (difference means subtract).

Question: Can you find two numbers which have a product of 20 and a sum of 12?

Answer: The two numbers that you are looking for are 10 and 2, beacuse 10 multiplied by 2 gives 20, and 10 added to 2 gives 12.

Question: How much greater is the product of 4 and 3 than the sum of 4 and 3?

Answer: First, find the product of 4 and 3 by multiplying them together to give 12.

Now work out the sum of 4 and 3 by adding them together to give 7.

Now subtract 7 from 12 to give 5.

Question: Can you find two numbers that have a sum of 13 and a product of 12?

Answer: The two numbers are 1 and 12 (since 1+ 12 = 13, and 1 times 12 is 12).

Question: Can you find two numbers which have a product of 8 and a sum of 6?

Answer: 4 and 2 are the answers, because 4 multiplied by 2 is 8 and 4 added to 2 is 6.

Question: Find sum of 5/9 and 11/9?

Answer: Just add the numerators and keep the denominator the same to give 16/9.

Question: How can I work out the product of 18 and 4?

Answer: All you need to do is 18 multiplied by 4 which is 72.

Question: Can you find two numbers which have a product of 8 and a sum of 7?

Answer: Yes, you can but the answers are not integers (whole numbers).

You will need to solve the simultaneous equations xy = 8 and x + y = 7.

Question: The product of 5 whole numbers is 3. What is the sum of these numbers?

Answer: Product means multiply, so the 5 whole numbers that multiply together to give 3 are 1,1,1,1 and 3 (that is fours 1's and one 3).

Since "sum" means "add," then 1 + 1 + 1 + 1 + 3 gives a final answer of 7.

Question: Can you find two numbers which have a product of 741 and sum of 70 ?

Answer: The two number you are looking for are 57 and 13.

This is beacause 57 multiplied by 13 gives 741, and 57 added to 13 gives 70.

Question: What are the two numbers that the sum is 12 and the product is 36?

Answer: Remember, sum means add and product means multiply.

The two numbers that answer this question are 6 and 6.

This is because 6 add 6 is 12, and 6 multiplied by 6 is 36.

Question: What is 1/3 the sum of six and three?

Answer: First of all, work out the sum of 6 and 3 by adding these together to give 9.

Now to find a third of something you divide by 3, so 9 divided by 3 is 3.

Question: What number pair has the sum of 5 product of 4?

Answer: Sum means add, and product means multiply.

Therefore the two numbers needed are 1 and 4, because 1 added to 4 is 5 and 1 multiplied by 4 is 4.

Question: The product of two numbers is 72 and the sum is 18, what are that two numbers?

Answer: The two numbers are 6 and 12, because 6 times 12 is 72, and 6 added to 12 is 18.

Question: Can you find two numbers that have a product of -18 and a sum of -7?

Answer: The two numbers are -9 and 2.

This is because -9 multiplied by 2 is -18, and -9 plus 2 is -7.

Question: Can you find a number which has a product of -14 and a sum of 5?

Answer: The two numbers are -2 and 7, since -2 times 7 is -14, and -2 + 7 is 5.

Question: What are the two numbers which have a sum and product of 1 and 9?

Answer: The sum can be found by adding 1 and 9 to give 10.

The product of 1 and 9 can be found by multiplying 1 and 9 to give 9.

Question: What is the sum of 2 and 7?

Answer: The two numbers needed to be added together if you are working out the sum.

So 2 + 7 = 9.

Question: What is the sum of 19 and 25 multiplied by their difference?

Answer: First, work out the sum of 19 and 25 by adding the two numbers together to give 44.

Next, find the difference of 25 and 19 by subtracting the numbers to give 6.

Now multiply 44 by 6 to give 264.

Question: What is the product of 0.009 & 2.84?

Answer: To find the product of any two numbers just multiply them.

0.009 multipled by 2.84 gives 0.02556.

Question: Can you find two numbers which have a product of 60 and a sum of 100?

Answer: The two numbers are not integers, so there is not an obvious answer.

You will need to solve the simultaneous equations xy = 60, and x + y = 100, to give x

The two answers are 99.3963 and 0.6036 rounded to 4 decimal places.

Question: What is the answer to halve the product of 5 and 12?

Answer: First of all work out the product of 5 and 12.

Therefore, multiply the 5 by the 12 to give 60 (since product means multiply).

Now half 60 to give a final of answer of 30.

Question: How can I work out the sum of 2/12 and 6/12?

Answer: To find the sum just add the two fractions together to get 8/12 which simplifies to 2/3.

Question: The product of two whole numbers is 648 and their sum is 51. What are the two numbers?

Answer: The two numbers are 24 and 27.

This is because 24 multiplied by 27 gives 648.

Also, 24 added to 27 gives 51.

Remember, product means multiply and sum means add.

Question: Can you find two numbers which have a sum of 13 and a product of 12?

Answer: Sum means add and product means multiply.

The two numbers are 1 and 12, as 1 + 12 = 13 and 1 multiplied by 12 gives 12.

Question: What is the product of 1 and 5?

Answer: Just multiply 1 by 5 to give an answer of 5.

Question: What’s the product of 7/12 and 14?

Answer: Convert 7/12 into a decimal by dividing 7 by 12 to give 0.583..., now multiply this by 14 to give 8.17 rounded to 2 decimal places or 49/6 if you prefer a fraction.

Question: What two numbers have a sum of 15 and a product of 36 ?

Answer: The answers are 3 and 12, since 3 + 12 = 15, and 3 multiplied by 12 is 36.

Question: What is the product of (3+20)(4-30)?

Answer: First, work out the brackets:

3 added to 20 gives 23, and 4 minus 30 gives - 26.

Now multiply 23 by -26 to give a final answer of -598.

Question: The square of a number is 81. Find the number?

Answer: There are two answers to this question.

The first one is 9, because 9 multiplied by 9 is 81.

The second answer is -9, because -9 multiplied by -9 is also 81 (two negatives multiplied together gives a positive answer).

Question: How can find the product of 3/5 and 42?

Answer: Probably best to convert 3/5 to a decimal first which is 0.6