Problem No. 14. Two sisters

There have been two sisters. When the older sister was asked about their age, she said: "We had 730 months in total, 7 years and 30 months ago. Also, you have to know that I am 7 years and 30 months older than my sister." How old is each of the sisters?

Student tip

First find their age, 7 years and 30 months ago.

Solution

First, 7 years and 30 months is equal to 114 months. Since, the older sister was 114 months older then her sister, and the sisters had together 730 months, 7 years and 30 months ago, we have that the younger sister had (730 - 114) / 2 = 308 m = 25 y 8 m, and the older sister had 308 + 114 = 422 m = 35 y 2 m, 7 years and 30 months ago. Today, after 7 years and 30 months, the younger sister  is the same age as the older sister 7 years and 30 months ago, i.e. the younger sister has 35 years and 2 months, and the older sister has 35 y 2 m + 7 y 30 m = 42 y 32 m = 44 y 8 m.