SOLUTION: Goliath is 12 years older than David.In six years, Goliath's age will be twice of David's age. How old is Goliath now?
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Question 119049: Goliath is 12 years older than David.In six years, Goliath's age will be twice of David's age. How old is Goliath now?
Answer by HyperBrain(694) (Show Source): You can put this solution on YOUR website!
Let x=Goliath's age
y=David's age
IF Goliath is 12 years older than David, THEN:
x=y+12
In six yrs, 6 yrs will be added to their present ages so
Let x+6=the age of Goliath in 6 yrs
y+6=the age of David in 6 yrs
SInce In six years, Goliath's age will be twice of David's age, then,
x+6=2(y+6)
But, we know that x=y+12. So,
(y+12)+6=2(y+6)---substitution
y+(12+6)=2(y+6)---associative property of addition
y+18=2(y+6)--------addition of integers
y+18=2y+2(6)-------distributive property of multiplication over addition
y+18=2y+12---------multiplication of integers
2y+12=y+18----------symmetric property of equality
2y+12-18=y+18-18----subtract 24 to both sides
2y-6=y+0------------subtraction of integers
2y-6=y----------------identity property of addition
2y-6+6=y+6------------add 6 to both sides
2y+0=y+6------------addition of integers
2y=y+6--------------identity property of addition
2y-y=y-y+6----------subtract y to both sides
y=0+6
y=6-----------------identity property of addition
Thus, the age of David is 6.
Since y=6 and x=y+12, then
x=6+12---substitution
x=18
The age of Goliath is 18.
The check is left to you.
Power up,
HyperBrain!
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