2022 AMC 12A Problem 2

Attempt Problem 2 of the 2022 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The sum of three numbers is

96.

The first number is

6

times the third number, and the third number is

40

less than the second number. What is the absolute value of the difference between the first and second numbers?

1

2

3

4

5

Let the third number be

t

and write the others in terms of

t

The first is

6t,

the second is

t+40,

and they sum to

96

Let the third number be

t.

Then the first is

6t

and the second is

t+40.

Their sum is

6t+(t+40)+t=8t+40=96,

t=7.

The first number is

42

and the second is

47,

so the difference has absolute value

5.

Thus, the correct answer is E.

Problem 2 in other years