Question

a) A woman is twice as old as her daughter. Five years ago the sum of their age was 62. What are their present ages.

b) A bottle is half full. After adding 275 mL to the bottle it is three quarters full. How much does the bottle hold when full?

Answer 1

A woman is twice as old as her daughter mean:

W = 2 D


Five years ago wooman was W - 5 yrs , daughter was D - 5 yrs

Five years ago the sum of their age was 62 mean:

W - 5 + D - 5 = 62

W - 10 + D = 62 Add 10 to both sides

W - 10 + D + 10 = 62 + 10

W + D = 72

Replace :
W = 2 D in this equation

2 D + D = 72

3 D = 72 Divide both sides by 3

D = 72 / 3 = 24 yrs

W = 2 D = 2 * 24 = 48 yrs


b)

V = Volume of a bottle

V / 2 + 275 = ( 3 / 4 ) V Subtract V / 2 to both sides

V / 2 + 275 - V / 2 = ( 3 / 4 ) V - V / 2

275 = ( 3 / 4 ) V - V / 2

275 = ( 3 / 4 ) V - ( 2 / 4 ) V

275 = ( 1 / 4 ) V Multiply both sides by 4

275 * 4 = ( 1 / 4 ) V * 4

1100 = V

V = 1100 mL