SOLUTION: Find three consecutive even integers such that the product of the first and second is 20 less than 10 times the third

Algebra.Com
Question 1200102: Find three consecutive even integers such that the product of the first and second is 20 less than 10 times the third
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Consecutive integers follow one after another.
Examples:
6,7,8
22,23,24

Consecutive even integers are when all of the values are even, and they are as close as possible.
Examples:
2,4,6
100,102,104

Let x be some integer. It might be even or odd.
To guarantee it is always even, we double it to 2x.
Eg:
x = 5 doubles to 2x = 2*5 = 10
x = 6 doubles to 2x = 2*6 = 12

2x = first even integer
2x+2 = even integer right after 2x
2x+2+2 = 2x+4 = even integer right after 2x+2

In short,
first = 2x
second = 2x+2
third = 2x+4

The sequence {2x,2x+2,2x+4} represents a set of three consecutive even integers, where x is any integer.

We then have the following information " the product of the first and second is 20 less than 10 times the third".

Let's translate that into an equation and solve for x.

first*second = 10*third - 20
2x*(2x+2) = 10*(2x+4) - 20
4x^2+4x = 20x+40 - 20
4x^2+4x = 20x+20
4x^2+4x-20x-20 = 0
4x^2-16x-20 = 0
4(x^2-4x-5) = 0
x^2-4x-5 = 0
(x-5)(x+1) = 0
x-5 = 0 or x+1 = 0
x = 5 or x = -1

Optionally you could use the quadratic formula to solve for x.
Let me know if you need to see these steps.

If x = 5, then,We end up with the set {10,12,14} as one solution.

If x = -1, then,We end up with the set {-2,0,2} as the other solution.


Check for the first solution:
first*second = 10*third - 20
10*12 = 10*14 - 20
120 = 140 - 20
120 = 120
The first solution set is confirmed.

Check for the second solution:
first*second = 10*third - 20
-2*0 = 10*2 - 20
0 = 20 - 20
0 = 0
The second solution set is confirmed.
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
n, n+2, n+4

-



Try to avoid quadratic formula general solution method.

Two factors differing by 8 to give product 20:
10 and 2.
n=10.

The consecutive even integers: 10, 12, 14.
RELATED QUESTIONS

find three consecutive even integers such that the product of the first and third is 20... (answered by BumbleStar,addingup,TeachMath)
Find three consecutive even integers such that the product of the first and the third is... (answered by mananth)
find three consecutive even integers such that the product of the first and third is 24... (answered by unlockmath)
find three consecutive even integers such that the product of the first and second is... (answered by CubeyThePenguin)
find three consecutive even integers such that the product of the first and the third... (answered by CubeyThePenguin)
Find three consecutive even integers such that six times the sum of the first and the... (answered by MathLover1)
find the second of the three consecutive positive even integers such that the product of... (answered by ewatrrr,MathLover1)
Find three consecutive positive even integers such that the product of the first and... (answered by checkley75)
Find three consecutive positive even integers such that the product of the second and... (answered by dabanfield)