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Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?

Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
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See a solution process below:

Explanation:

First, lets call:

#a# the number of pounds of apples Mo sold.

#p# the number of pounds of peaches Mo sold.

Then we can write these two equations from the information in the problem:

Equation 1: #a + p = 165#

Equation 2: #1.75a + 2.50p = 337.50#

Step 1) Solve the first equation for #a#:

#a + p = 165#

#a + p - color(red)(p) = 165 - color(red)(p)#

#a + 0 = 165 - p#

#a = 165 - p#

Step 2) Substitute #(165 - p)# for #a# in the second equation and solve for #p#:

#1.75a + 2.50p = 337.50# becomes:

#1.75(165 - p) + 2.50p = 337.50#

#(1.75 xx 165) - (1.75 xx p) + 2.50p = 337.50#

#288.75 - 1.75p + 2.50p = 337.50#

#288.75 + (-1.75 + 2.50)p = 337.50#

#288.75 + 0.75p = 337.50#

#-color(red)(288.75) + 288.75 + 0.75p = -color(red)(288.75) + 337.50#

#0 + 0.75p = 48.75#

#0.75p = 48.75#

#(0.75p)/color(red)(0.75) = 48.75/color(red)(0.75)#

#(color(red)(cancel(color(black)(0.75)))p)/cancel(color(red)(0.75)) = 65#

#p = 65#

Because the problem only asks for the number of pounds of peaches we do not need to go any further.

Mo sold #color(red)(65)# pounds of peaches.

answered by: smendyka
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Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
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