Question 1170837: In eight years, Monica will be 4/5 the age of her brother Mario. Four years ago, Monica was half as old as her brother. How old is Mario?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source):
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
Let x be the age of Monica an
y be the age of Mario.
The first statement "In eight years, Monica will be 4/5 the age of her brother Mario", means, by DEFAULT
"In eight years, Monica will be 4/5 the age of her brother Mario at that time".
The precise mathematical translation is THIS exaction
x + 8 =  .
Simplify this equation
5x + 40 = 4(y + 8)
5x + 40 = 4y + 32
5x - 4y = -8 (1)
The second statement "Four years ago, Monica was half as old as her brother", means, by DEFAULT,
"Four years ago, Monica was half as old as her brother at that time".
The precise mathematical translation is THIS exaction
x - 4 =  .
Simplify this equation
2x - 8 = y - 4
2x - y = 8 - 4
2x - y = 4 (2)
To solve the system of two equations (1) and (2), express y = 2x - 4 from (2) and substitute it into (1). You will get then
5x - 4*(2x-4) = -8, or
5x - 8x + 16 = -8
-3x = -8 - 16 = -24,
x = 8.
Then from equation (2), y = 2*8 - 4 = 16 - 4 = 12.
ANSWER. Mario is 12 years old.
Solved.
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