Question

1.Nancy is 3 times as old as Cathy. In seven years, she will be ten years older than Cathy. What are their present age?

Answer 1

N = Present Nancy ages

C = Present Cathy ages


Nancy is 3 times as old as Cathy mean:

N = 3 C


In seven years Nancy will be N + 7 yrs old , Cathy will be C + 7 yrs old


In seven years, she will be ten years older than Cathy Mean:

N + 7 = C + 7 + 10

N + 7 = C + 17 Subtract 7 to both sides

N + 7 - 7 = C + 17 - 7

N = C + 10

Replace N = 3 C in this equation

3 C = C + 10 Subtract C to both sides

3 C - C = C + 10 - C

2 C = 10 Divide both sides by 2

C = 5 yrs

N = 3 C = 3 * 5 = 15 yrs


Proof:

In seven years, Nancy will 15 + 7 = 22 yrs old

Cathy will be 5 + 7 = 12 yrs old

22 - 12 = 10 yrs