SOLUTION: A set of three positive integers has a sum of 9 and a product of 24. If the smallest of the integers is 2, what is the largest? a.)12 b.)8 c.)6 d.)4 e.)2

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: A set of three positive integers has a sum of 9 and a product of 24. If the smallest of the integers is 2, what is the largest? a.)12 b.)8 c.)6 d.)4 e.)2      Log On


   

Question 896659: A set of three positive integers has a sum of 9 and a product of 24. If the smallest of the integers is 2, what is the largest?
a.)12 b.)8 c.)6 d.)4 e.)2
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
m,n,p the integers.

One of them is 2.
The integers are m, n, and 2.

m%2Bn%2B2=9
highlight_green%28m%2Bn=7%29

mn%2A2=24
highlight_green%28mn=12%29

Highlighted in green%28GREEN%29 are two equations in two unknown variables.
Do you know how to continue and finish this?

---
m%2Bn=7
n=7-m
-
Substitute into the product equation.
m%2An=12
m%2A%287-m%29=12
7m-m%5E2=12
-m%5E2%2B7m=12
-m%5E2%2B7m-12=0
m%5E2-7m%2B12=0%2C factorable.
%28m-3%29%28m-4%29=0
m=3 OR m=4
Correspondingly computing or evaluating n, you find that n=4 or n=3.

The two unknown integers are 3 and 4.
The integer, 2, was already given.