Question

Joan, Kylie, Lillian, and Miriam all celebrate their birthdays today. Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women today?

A. 51
B. 52
C. 53
D. 54
E. 55

Answer 1

d) 54

Explanation:

Let's name x the age of Kylie.

Then we have:

K = x

Joan is 2 years younger than Kylie ⇒ J = x - 2

Kylie is 3 years older than Lilian ⇒ L = x - 3

Miriam is one year older than Joan ⇒M = (x - 2) + 1 = x - 1

If we sum up all ages we get: x + x -2 + x - 3 + x - 1 = 4x - 6

Therefore, the sum of all ages is 4x - 6.

Let's make x = 14 ⇒ 4x - 6 = 4(14) - 6 = 50

Let's make x = 15 ⇒4x - 6 = 4(15) - 6 = 54

Let's make x = 16 ⇒4x - 6 = 4(16) - 6 = 58

If we substitute for smaller x, we'll get values smaller than 50 and if we substitute for x >16 we'll get values greater than 58.

Looking at the options given by the problem, we can see that the only one that fits into the equation is d) 54.