# Mathematics

posted by .

The difference between two numbers is 9 and the product of the numbers is 162. Find the two numbers. Explain your working

• Mathematics -

Let x be the larger number
x*(x-9) = 162

Rearrange and factor
x^2 - 9x -162 = 0
(x+9)(x - 18) = 0
Take it from there.

There will be two pairs of solutions.

• Mathematics -

By symbols

A-B=9

AxB=162

so A=9+B

(9+B)B=162

9B+B^2=162

B^2+9B-162=0

so B=-18 or 9

correspondingly from AxB=162

A=-9 or 18

check against A-B=9

-9--18=9

18-9=9

## Similar Questions

1. ### math-word problems with quadratics

I have 5 questions... 1) The sum of two numbers is 12. Their product is 36. Find the two numbers. 2) The sum of two numbers is -15. Their product is -100. Find the two numbers. 3) The sum of two numbers is -8. Their product is 12. …
2. ### Reiny! Reiny! Reiny! Answer Check and HW Help!

Translate to a system of equations and solve: 1) The sum of two numbers is 36. One number is 2 more than the other. Find the numbers. Answer: (17,19) 2) Find two numbers whose sum is 66 and whose difference is 18. Answer: (37,29) These …
3. ### algebra

Stacey throws two dice. The difference in face value between the two dice is three, and the product of the numbers thrown is equal to twice the sum of the two numbers. Show and solve an alebraic equation that finds the numbers Stacey …
4. ### Algebra

kaylin throws two dice. the difference in face value between the two dice is three, and the product of the numbers thrown is equal to twice the sum of two numbers. Write and solve an algebraic equation that finds the numbers kaylin …
5. ### math

Mr burr the head custodian is working on putting new numbers on 42 of the 81 classroom doors. He found two numbers for the 23rd door he was working on in the 6th grade hallway whose sum is 35 and their product is 306. What are the …

1.Tasha believes that she can rewrite the difference 120-36 as a product of the GCF of the two numbers and another difference.Is she correct?
7. ### Maths- Proof

The question is: Prove algebraically that the difference between the squares of any two consecutive even numbers is always a multiple of 4. My working was: Let the numbers be n and n + 2 (n+2)^2 - (n)^2 =n^2 + 4n + 4 - n^2 =4n + 4 …
8. ### mathematics-Algebra

I think of two whole numbers;the product of the average of the sum and difference of the numbers and the difference of the sum and difference of the numbers is 12.if three times the first added to the second makes up 11..find the two …
9. ### Math

Difference between two numbers is 5 and the product is 6 find the numbers
10. ### math

the difference between the sum of the two numbers and the difference of the two numbers is 6.Find the larger of the two numbers if their product is 15

More Similar Questions