SOLUTION: Gary bought 3/5 as many apples as oranges from the supermarket. He gave away 6 apples and 26 oranges. He then had 3/4 as many apples left as oranges. How many apples and oranges di

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Gary bought 3/5 as many apples as oranges from the supermarket. He gave away 6 apples and 26 oranges. He then had 3/4 as many apples left as oranges. How many apples and oranges di      Log On


   

Question 1184922: Gary bought 3/5 as many apples as oranges from the supermarket. He gave away 6 apples and 26 oranges. He then had 3/4 as many apples left as oranges. How many apples and oranges did Gary buy altogether?
Found 3 solutions by greenestamps, JBnovelwriter, josgarithmetic:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


You might set this problem up for solving by letting x be the number of oranges, making the number of apples (3/5)x. If you are careful you should end up with the right answer.

I would prefer setting the problem up without fractions at the very beginning. So I would do this:

let 5x = # of oranges
let 3x = # of apples

Then 5x-26 is the number of oranges he ends up with; and 3x-6 is the number of apples he ends up with.

The number of apples he ends up with is 3/4 the number of oranges he ends up with:

3x-6=%283%2F4%29%285x-26%29
4%283x-6%29=3%285x-26%29
12x-24=15x-78
54=3x
x=18

ANSWER: The total number of apples and oranges he bought was 5x+3x = 8x = 8*18 = 144

CHECK:
oranges: started with 5x=90; gave away 26, ending with 64
apples: started with 3x=54; gave away 6, ending with 48
48/64 = 3/4

Answer by JBnovelwriter(34) About Me  (Show Source):
You can put this solution on YOUR website!
a= apples b=oranges
%283%2F5%29b=a
a-6=%283%2F4%29%28b-26%29
You have what a equals so replace a in 2nd equation
%283%2F5%29b-6=%283%2F4%29%28b-26%29
Now we start solving for b
Go ahead and do the reciprocal of 3/4 so times by 4/3 to each side
%284%2F3%29%283%2F5%29b-%284%2F3%29%286%29=b-26 left side 3s cancel and the 6 becomes a 2
%284%2F5%29b-8=+b-26 lets get rid of the 26 to isolate one variable add 26 to each side.
%284%2F5%29b%2B18=b lets get rid of the other fraction so multiply both sides by 5
4b%2B90=5b subtract 4b from both sides
90=b now take this value and put in the first equation
%283%2F5%29b=a
%283%2F5%29%2890%29=a the 90 can be reduced by the 5 to 18 (18*5=90) and (3*18=54)
54=a
54 apples 90 oranges
Total of 144 fruits

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
n number of oranges

Apples: 3n%2F5
Oranges: n


Gave-away

Apples: 3n%2F5-6
Oranges: n-26


had 3/4 as many apples left as oranges.
%283n%2F5-6%29%2F%28n-26%29=3%2F4 or better, %283%2F4%29%28n-26%29=3n%2F5-6.

---

LCD, 4%2A5
4%2A5%2A%283%2F4%29%28n-26%29=4%2A5%2A%283n%2F5-6%29
15%28n-26%29=12n-120
15n-15%2A26=12n-120
3n=15%2A26-120
3n=270
highlight%28n=90%29 and then ,.....