A local market wants to mix some $5 apples with some $4 oranges. (These cost are per pountd) How many pounds of each item should they mix to obtain a 30 pound mixture that sells for $4.40 per pound?

Question

A local market wants to mix some $5 apples with some $4 oranges.   (These cost are per pountd)   How many pounds of each item should they mix to obtain a 30 pound mixture that sells for $4.40 per pound?

anonymous · Answer

do i use elimination?

whpalmer4 · Answer

you can solve the equations with substitution or elimination...the trick is setting up the equations in the first place.

jhannybean · Answer

I had written it wrong earlier, sorry about that.

anonymous · Answer

wait, so is it x+y=30 
                   5x+4y=4.40?

whpalmer4 · Answer

no, it has to be 5x + 4y = 30*4.40 — the value of the fruit is what the total amount will sell for.

anonymous · Answer

sorry but i don't quite get it .....

whpalmer4 · Answer

they sell apples for $5/lb.  they sell oranges for $4/lb.  they want to put together 30 lbs of fruit in a mixture that they can sell for $4.40/lb.  The total selling price is 30*$4.40, just as if they had sold them separately in the proper proportions.  so, if x is the number of apples, and y is the number of oranges, $5/lb *x + $4/lb * y = 30*$4.40.

anonymous · Answer

so oranges=18 
and apples=12?

whpalmer4 · Answer

let's check:

18+12 = 30 so far so good
$5/lb * 12 lb + $4/lb *18 lb = 30 lb*$4.40/lb
$60 + $72 = $132
looks good!

anonymous · Answer

all right. thanks for the help :)