Find three consecutive even integers that the sum of twice the smallest number and three times the largest is 42

Answer 1

Find three consecutive even integers that the sum of twice the smallest number and three times the largest is 42

Let N = the first even integer

Let N + 2 = the second consecutive even integer

Let N + 4 = the third consecutive even integer

"Twice the smallest" translates to "2N".

"Three times the largest" translates to "3(N + 4)".

"Sum" translates to "+".

"is 42" translates to "= 42".

2N + 3(N + 4) = 42 Our Equation

2N + 3N + 12 = 42 Multiplying 3 times N and 3 times 4.(Distributive property)

5N + 12 = 42 Combining the N's.

5N + 12 - 12 = 42 - 12 Subtracting 12 from both sides to isolate the variable N.

5N = 30

5N/5 = 30/5 Dividing both sides by 5 to isolate the variable N.

N = 6

First even number is 6.

Second consecutive even number is N + 2 = 6 + 2 = 8

Third consecutive even number is N + 4 = 6 + 4 = 10

ANSWER: 6, 8, 10

CHECKING:

Does 2N + 3(N + 4) = 42?

(2)(6) + 3(6 + 4) = 12 + (3)(6) + (3)(4) = 12 + 18 + 12 = 30 + 12 = 42

Yes it does.

Hope this helps you Anthony.