# algebra

posted by .

the product of two consecutive even integersis 34 less than 7 times their sum.find the two integers.

• algebra -

let the first integer be x
then the second even integer is x+2

x(x+2) = 7(x + x+2) - 34
x^2 + 2x = 14x + 14 - 34
x^2 - 12x + 20 = 0
(x-10)(x-2) = 0
x = 10 or x = 2

the numbers are 10 and 12 or the numbers are 2 and 4

check:
case 1: numbers are 10 and 12
product = 120
7 times their sum = 154
is 120 less than 154 by 34 ? YES

case 2: numbers are 2 and 4
product = 8
7 times their sum = 42
is 8 less than 42 by 34 ? YES!

the integers could be 10 and 12
or
the integers could be 2 and 4

## Similar Questions

1. ### Algebra

Find two consecutive even integers that have a sum of 450. 224+226=450 If two consecutive even integers, x and x + 2, add up to 450, then 2x + 2 = 450 2x = 448 x = 224 is the smallest of the two. Okay thanks.
2. ### algebra

Five times the smallest of three consecutive odd integers is ten more than twice the longest. Find the integers. The sum of three integers is one hundred twenty three more than the first number. The second number is two more than the …
3. ### Algebra II

Find 4 consecutive odd integers such that 5 times the sum of the first two was 10 less than 7 times the sum of the second and fourth. What are the four integers?
4. ### mathematics

Three times the reciprocal of the sum of two consecutive odd integers is 3/20. Find the two consecutive off integers.
5. ### Algebra

The sum of the squares of two consecutive positive even integers is one hundred sixty-four. Find the two integers.
6. ### math

A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided …
7. ### Math

1. if the largest of three consecutive even integers is multiplied by 5, the product is 6 less than three times the sum of the first two integer. fin the integers.
8. ### math

What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest?
9. ### math

What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest?
10. ### math

the sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers

More Similar Questions