Answer: $180
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Work Shown:
x = total allowance
x/3 = amount saved
2x/3 = amount spent
x-80 = amount left over after spending $80 on food
(2/5)*(x-80) = amount spent on stationary
80+(2/5)(x-80) = total amount spent
80+(2/5)(x-80) = 2x/3
Multiply both sides by the LCD 15 to clear out the fractions
15*( 80+(2/5)(x-80) ) = 15*( 2x/3 )
1200 + 6(x-80) = 10x
1200+6x-480 = 10x
720+6x = 10x
720 = 10x-6x
720 = 4x
4x = 720
x = 720/4
x = 180
Kenny's allowance is $180
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Check:
He saves 1/3 of his $180 allowance, so he saves (1/3)*180 = 60 dollars and spends 180-60 = 120. In other words, (2/3)*180 = 120 is spent.
$80 of the 120 is spent on food, which means the remaining 120-80 = 40 dollars spent on stationary.
If he starts off at $180 and spends $80 on food, then that's a difference of 180-80 = 100 dollars. Two-fifths of which is (2/5)*100 = 40 dollars to match the amount spent on stationary. This helps confirm we have the correct answer of $180.