## anonymous one year ago 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? • This Question is Closed 1. anonymous 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

2. anonymous

why wouldnt it be 1/3x (2/5x)

3. anonymous

4. anonymous

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

5. anonymous

i dont get it can u give me a visual and draw something?

6. anonymous

hey y do u have it multiplied by 1/3 instead of 2/3?

7. anonymous

because the question says he spent 1/3 of his remaining at the toy store not 2/3

8. anonymous

but isnt the remaining 2/3?

9. anonymous

we use what he spent, not what is remaining

10. anonymous

he spent 1/3 of his allowance AFTER he spent the 3/5

11. anonymous

you dont use the remaining allowance to calculate

12. anonymous

|dw:1440706845056:dw|

13. anonymous

you dont use the remaining. you use the spent fraction...

14. 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 $\frac{3x}{5} + \frac{2x}{15 }+0.80= x$

15. anonymous

oh okay i get it now lol thanks phi

16. phi

to solve, multiply both sides and all terms by 15 (this will get rid of the fractions) $9x + 2x + 15\cdot 0.8 = 15 x \\ 15 \cdot 0.8 = 4 x\\ x= \frac{15 \cdot 0.8}{4} = 15 \cdot 0.2 = 3.00$

17. anonymous

ohhhhh okay got it now that was a good explanation