SOLUTION: A box of apples costs $2,a box of pears costs $3,and a box of plums costs $4.If 8 fruit boxes cost $23 together, what is the largest possible number of them that contain plums?

Question 298977: A box of apples costs $2,a box of pears costs $3,and a box of plums costs $4.If 8 fruit boxes cost $23 together, what is the largest possible number of them that contain plums?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A box of apples costs $2,a box of pears costs $3,and a box of plums costs $4.
If 8 fruit boxes cost $23 together, what is the largest possible number of them that contain plums?
:
Let x = no. of boxes of apples
Let y = no. of boxes of pears
Let z = no. of boxes of plums
:
no. of boxes equation
x + y + z = 8
:
total cost equation
2x + 3y + 4z = 23
:
Looks like 3 boxes of plums would be the max, see if that will work
Cost for 3 boxes = $12
:
Adjust the equations to reflect 3 boxes of plums
x + y = 8 - 3
x + y = 5
y = (5-x)
and
2x + 3y = 23 - 12
2x + 3y = 11
Replace y with (5-x)
2x + 3(5-x) = 11
2x + 15 - 3x = 11
2x - 3x = 11 - 15
-x = -4
x = 4 boxes of apples
then
5 - 4 = 1 boxes of pears
:
We can't have less than 1 box of pears, so it has to be 3 boxes of plums
:
Check solutions
4 + 1 = 3 = 8
and
2(4) + 3(1) + 4(3) = 23
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