Question

Lindsay is \[5\] years younger than Mark. Seven years ago, the sum of their ages was \[31\]. Let \[l\] be Lindsay's age, and let \[m\] be Mark's age.

A) \[l + m = 27\]
B) \[l + m = 33\]
C) \[l + m = 36\]
D) \[l + m = 41\]

Answer 1

Lindsay is 20 years old and Mark is 25 years old. The sum of their ages is 45. None of the given answer choices match the correct sum.

Step-by-step explanation:

Let's denote Mark's age as m and Lindsay's age as l.

According to the problem, Lindsay is 5 years younger than Mark, so we can write the equation: l = m - 5.

Seven years ago, the sum of their ages was 31. We can represent this equation as: (l - 7) + (m - 7) = 31.

By substituting the value of l from the first equation into the second equation, we get: (m - 5 - 7) + (m - 7) = 31. Simplifying this equation gives us 2m - 19 = 31. Solving for m, we find that m = 25. Therefore, l = m - 5 = 25 - 5 = 20.

The sum of their ages is l + m = 20 + 25 = 45.

Therefore, none of the answer choices (A, B, C, D) match the correct sum of their ages, which is l + m = 45.