SOLUTION: Hi fiona is holidaying in Europe. After a week she has spent 2/5 of her spending money. The following week she spends 630 dollars and calculates that she has 1/4 of her money lef

Question 1052808: Hi
fiona is holidaying in Europe. After a week she has spent 2/5 of her spending money. The following week she spends 630 dollars and calculates that she has 1/4 of her money left.what was her original
amount of money.
My answer was 4200 dollars the textbook solution was 1800 dollars. Who is correct?
Thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this one is tricky.

let x equal her original spending money.

after the first week she spent 2/5 of that.

what she has left is 3/5 * x.

the following week she spends 630 dollars and calculates that she has 1/4 of her spending money left.

i believe they mean 1/4 of her original spending money left.

the only way i know that is because it makes the answer come out what they said it should come out.

she starts with x.

after one week she spends 2/5 * x.

therefore she has 3/5 * x left.

after two weeks she spends an additional 630 dollars and has 1/4 * x left.

the formula for this would be 3/5 * x - 630 = 1/4 * x

solve for x as follows:

start with 3/5 * x - 630 = 1/4 * x

subtact 1/4 * x from both sides of the equation and add 630 to both sides of the equation to get 3/5 * x - 1/4 * x = 630

3/5 is equal to 12/20 and 1/4 is equal to 5/20.

the equation becomes 12/20 * x - 5/20 * x = 630

combine like terms to get 7/20 * x = 630

solve for x to get x = 20/7 * 630 = 1800.

if the original amount is 1800, then she spent 2/5 of that.

this means she spent 720 dollars.

1800 - 710 = means she had 1080 left.

she then spent 630 which means she had 1080 - 630 = 450 left.

450 is equal to 1/4 * 1800.

if the original amount is 4200, and she spent 2/5 of that in the first week, then she had 3/5 * 4200 = 2520 left.

she then spent 630 which means she had 1890 left.

1890 is not equal to 1/4 * 4200.

doesn't compute.

if you can explain to me how you got 4200 then i might be able to explain to you what you did wrong.

i think what you might have done is say that 2/5 * x was remaining.

if that's the case, then you would get 2/5 * x - 630 = 1/4 * x.

if you solved for x in that case, then you would get 4200.

unfortunately, what remained after the first week was 3/5 * x and not 2/5 * x.

2/5 * x is what was spent in the first week.

i give it to the book this time.

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