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?
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?
Answers
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
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
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