find three consecutive integers

Question

find three consecutive integers such that the sum of the first and twice the second is 122 minus three times the third.

Answer 1

Let x = the first number

x + 1 = the second number

x + 2 = the third number

Then,

x +2(x+1) = 122 - 3(x+2) or 6x = 114 or x = 19

So, the numbers are 19, 20, & 21

Answer 2

There's a few steps for this one. The first is to translate the question into some kind of equation we can solve. Let a, b, c be the three numbers, then we have that:

a + 2b = 122-3c

However, we can't solve one equation with three variables, so we have to somehow get rid of two of them. This is where we can use the "consecutive" part of the question. Since the numbers are consecutive, we can write

b = a+1

c = a+2

Substituting these values into the first equation should let us solve for a, which would then give us the other two values!