Find two numbers whose sum in 25 if the product of one by the square of the other is to be maximum

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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 2 less than the sum of 100 and 17?

Answer: 100 + 17 = 117.

117 - 2 is 115.

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

0.6 multiplied by 42 is 25.2.

Question: What two numbers have the product of 20 and the quotient of 5?

Answer: Product means the two numbers need to multiply to give 20, and quotient means the two numbers must divide to give 5.

Therefore, the answers are 10 and 2, becuase 10 multiplied by 2 is 20, and 10 divided by 2 is 5.

Question: What is the sum of 3/x + 2/5, x is not equal to 0?

Answer: Make a common denominator of 5x.

So multiply the numerator and denominator of the first fraction by 5 to give 15/5x.

Also multiply the numerator and denominator of the second fraction by x to give 2x/5x.

Now add these together to give (15 + 2x)/5x.

Question: What is the sum of 5 and 17?

Answer: 22 since you add the numbers.

Question: What is the product of -1.24 and 4.25?

Answer: Just multiply the numbers together to give -5.27.

Question: The product of two numbers is 3 and their sum is –4. Therefore the two numbers are?

Answer: The two numbers are -1 and -3, since -1 multiplied by -3 is 3 and -1 add -3 is -4.

Question: what number is 76 more than the product of 13 and 26?

Answer: 13 multiplied by 26 is 338.

338 added to 76 gives 414.

Question: How do you find the product of 1/4m²(8m²-4)?

Answer: First multiply 1/4m^2 by 8m^2 to give 2m^4.

Next multiply 1/4m^2 by -4 to give -m^2.

So the final answer is 2m^4 - m^2.

Question: 2 numbers have a difference of 18 and a product of -65 ?

Answer: The two numbers are -13 and 5.

Question: What is the sum of 9.8 and 573.54?

Answer: Just add the numbers together to give 583.34.

Question: Find two numbers that have the product of 42 and a sum of 17?

Answer: The two numbers are 3 and 14.

This is because they multiply to give 42 and add to give 17.

Question: A pair of numbers with a sum of 18 and the difference of two?

Answer: 8 and 10 are the two numbers, since 8 plus 10 is 18 and 10 minus 8 is 2.

Question: Find the product of 15 and 7?

Answer: Just multiply 15 by 7 to give 105, since product means times.

Question: What is the sum of 7, 4 and 12?

Answer: Just add all of the numbers up, 7 + 4 + 12 = 23.

Question: Can you find the answer for 2+3×4=?

Answer: You need to use BIDMAS or BODMAS.

First work out the multiplication to give 12.

Now 2 + 12 =14.

Question: What is the sum and product of 8 and 45?

Answer: To find the sum add up the two numbers, 8 + 45 gives 53.

To find the product multiply 8 by 45 to give 360.

Question: What are the two numbers with a sum of 34 and a product of 225?

Answer: 9 and 25, since 9 added to 25 is 34, and 9 times 25 is 225.

Question: What is the product -28 and the sum of 3?

Answer: The two numbers are 7 and -4, because 7 times -4 is -28 and -4 + 7 is 3.

Question: Can you find two numbers with a sum of -2 and a product of -48?

Answer: -8 ad 6 are the answers, as -8 + 6 is -2 and -8 times 6 is -48.

Question: Can you find the product of -13, 12 and -5?

Answer: You just need to multiply the three numbers together in any order.

-13 times 12 is -156.

-156 times -5 is 780.

Question: Which integer should be multiplied by -7 so as to get a product equal to 56?

Answer: The answer is -8 as -7 times -8 is 56.

Question: What are the two integers whose sum is 14 and product is 33?

Answer: The two integers are 3 and 11, since 3 add 11 is 14, and 3 multiplied by 11 is 33.

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: 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: 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: 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: 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 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: 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: 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: 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: 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: 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: 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: 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 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: 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’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 is the product of 1 and 5?

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

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.

© 2011 Mark

Rachel Simpson on April 30, 2020:

What is the product of 2,3and 4