PSAT Math Multiple-Choice Question 555: Answer and Explanation

Question: 555

A two-digit number has a tens place, t, and a units place, u. The digits have the following relationships:

t + u = 8

t = 2 + u

What is the value of the two-digit number given by these two digits?

• A. 41
• B. 53
• C. 63
• D. 79

Correct Answer: B

Explanation:

(B) Use substitution to solve for t and u:

t + u = 8

t = 2 + u

Plug in 2 + u for t into the first equation:

(2 + u) + u = 8

2 + 2u = 8

2u = 6

u = 3

Plug in 3 for u into one of the original equations, and solve for t. This gives 5 in the tens place and 3 in the ones place, making 53 your answer.

Alternatively, you can solve this using elimination.

t + u = 8

t = 2 + u

Rearrange the second equation:

t = 2 + u

t - u = 2

Then you have this as the set of equations:

t + u = 8

t - u = 2

Add the two together to get:

2t = 10

t = 5

Then substitute t = 5 into the first equation to solve for u:

t + u = 8

5 + u = 8

u = 3

The answer is still 53.