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?
+128407 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
