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In preparation for a graduation party, Christine bought peaches, oranges, and bananas. Peaches cost \$1.50 each, oranges cost \$1.00 each, and bananas cost \$0.50 each. A total of \$87.50 was spent on the fruit, and 91 pieces of fruit were purchased. If \$26.50 more was spent on peaches than on bananas, how many peaches were purchased?

Feb 28, 2020

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I actually did it wrong...

Feb 28, 2020
edited by brianlaw  Feb 28, 2020
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Let  x  be the number  of peaches, y  the  number of oranges and z the  number  of bananas

We  have  this system

x + y + z  =   91       (1)

1.5x  + 1y + .5z  = 87.50    (2)

1.5x - .5z  = 26.50      (3)

Rearrange  (3)  as

.5z  = 1.5x  -  26.50   (4)

And  subbing  this  into 2  we  have  that

1.5x + y  +  [ 1.5x - 25.50 ]  = 87.50    simplify

3x  + y  -  26.50  =  87.50

3x  +  y =  114

y = 114  - 3x  (5)

Multiply  (4) through  by 2

z = 3x - 53   (6)

Sub (5) and (6)  into (1)  and  we have that

x + (114 -3x)  + (3x - 53)  =  91

x  +  61 =  91    subtract 61  from both sides

x =  30  = the number of peaches bought

Feb 28, 2020
edited by CPhill  Feb 28, 2020