SOLUTION: Don runs a charity fruit sale, selling boxes of oranges for $11 and boxes of grapefruit for $10. If he sold a total of 762 boxes and his total income was $8125, how many boxes of o
Question 103106: Don runs a charity fruit sale, selling boxes of oranges for $11 and boxes of grapefruit for $10. If he sold a total of 762 boxes and his total income was $8125, how many boxes of oranges did he sell.
X= boxes of oranges y=boxes of grapefruit
$11x+10y=$8125
this is as far as I've gotten in attempting to solve the problem. Answer by doukungfoo(195) (Show Source):
You can put this solution on YOUR website! So far so good.
You have the first equation set up correctly:
11x+10y=8125
Now we need to write another equation from the given information.
Given: Don sold a total of 762 boxes.
So if x = boxes of oranges
and y = boxes of grapefruit
then
x + y = 762
Now we have a system of equations that we can use to solve for x and y
First equation: 11x + 10y = 8125
Second equation: x + y = 762
Set the the second equation equal to x
x + y = 762
x = 762 - y
Now that we have x equal to 762-y we can subsitute that into the first equation and solve for y
11x + 10y = 8125
11(762-y) + 10y = 8125
8382 - 11y + 10y = 8125
8382 - y = 8125
-y = -257
y = 257 Answer: Don sold 257 boxes of grapefruit
Now use this to find the number of orange boxes sold
x + y = 762
x + 257 = 762
x = 505 Answer: Don sold 505 boxes of oranges
Check both answers in both equations
first equation:
11x + 10y = 8125
11(505) + 10(257) = 8125
5555 + 2570 = 8125
8125 = 8125
Good that works now try the second equation
x + y = 762
505 + 257 = 762
762 = 762
that works too so we know that we have correctly solved this problem.
