Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

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Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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if his allowance is x, 3x/5 = allowance on arcade this means that there is 2x/5 remaining 1/3(2x/5) = toy store => 2x/15 = toy store adding 3/5 and 2/15 we get a total amount spent of 11x/15 of his allowances. this must mean that there is only 4x/15 remaining. since his last bit of money was .80, we can say 4x/15 = .80. solving for x we have x = $3.00
why wouldnt it be 1/3x (2/5x)
and y do u multiply instead of adding

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because read the question again, he spent 3/5 at the arcade, then he spent 1/3 (emphasis on THIRD) on his REMAINING allowance, not 1/5 of his total allowance, which is why you multiply
i dont get it can u give me a visual and draw something?
hey y do u have it multiplied by 1/3 instead of 2/3?
because the question says he spent 1/3 of his remaining at the toy store not 2/3
but isnt the remaining 2/3?
we use what he spent, not what is remaining
he spent 1/3 of his allowance AFTER he spent the 3/5
you dont use the remaining allowance to calculate
|dw:1440706845056:dw|
you dont use the remaining. you use the spent fraction...
  • phi
let x be the allowance 3/5 of his allowance is 3x/5 (2x/5 is remaining) 1/3 of his remaining is 1/3 of 2x/5 = 2x/15 0.80 is left over the sum of these 3 must add up to the whole allowance \[ \frac{3x}{5} + \frac{2x}{15 }+0.80= x \]
oh okay i get it now lol thanks phi
  • phi
to solve, multiply both sides and all terms by 15 (this will get rid of the fractions) \[ 9x + 2x + 15\cdot 0.8 = 15 x \\ 15 \cdot 0.8 = 4 x\\ x= \frac{15 \cdot 0.8}{4} = 15 \cdot 0.2 = 3.00\]
ohhhhh okay got it now that was a good explanation

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