Question

10 years ago Mrs. Smith’s age was 17 times her daughter Angela’s age. 6 years later, Mrs. Smith’s age would be 4 years less than three times Angela’s age. Assuming Mrs. Smith’s present age as x years and Angela’s age as y years, frame two linear equations to model this situation and also find their present ages.

Answer 1

To find their present ages, two linear equations can be set up and solved simultaneously.

Step-by-step explanation:

To solve this problem, let's define Mrs. Smith's present age as x years and Angela's present age as y years. We are given two pieces of information: 10 years ago, Mrs. Smith's age was 17 times Angela's age, and 6 years later, Mrs. Smith's age would be 4 years less than three times Angela's age.

Using these two pieces of information, we can write two linear equations. The first equation is: x - 10 = 17(y - 10) (Mrs. Smith's age 10 years ago was 17 times Angela's age 10 years ago). The second equation is: x + 6 = 3(y + 6) - 4 (Mrs. Smith's age 6 years later would be 4 years less than three times Angela's age 6 years later).

To find their present ages, we can solve these two equations simultaneously.