Question

Please show all steps in order and in legible writing.

A woman is now 30 years older than her son. 15 years ago, she was twice as old. What are the present ages of the woman and her son?

Let x = age of the woman now

Let y = age of the son now

1) Set up equation 1 which containes x and y

2) Set up equation 2 which containes x and y

3) Solve for x and y

Answer 1

Present age of woman = x years old
Present age of son = y years old

woman is now 30 years older than her son

x=y+30.........(1)

15 years ago

woman was = x-15 years old

son was = y-15 years old

Then

she was twice as old.

x-15=2(y-15)

x-15=2y-30

x=2y-30+15

x=2y-15...........(2)

compare both equation

y+30=2y-15

y-2y=-15-30

-y=-45

y=45

Put the value of s in (1)

x=y+30.........(1)

x=45+30

x=75

.

Present age of woman = x = 75 years old
Present age of son = y = 45 years old