SOLUTION: Please help me with some word problems. I have tried for several hours and cant figure out where to begin. A citrus fruit company plans to make 13.25 pound gift box of oranges

Question 153481: Please help me with some word problems. I have tried for several hours and cant figure out where to begin.
A citrus fruit company plans to make 13.25 pound gift box of oranges and grapefruit. Each box cost $21. An orange weighs .5 pound and sells for $.75. Each grapefruit weights .75 pounds and sells for $1.25. How many oranges and grapefruit should be in each box?
Thank you.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A citrus fruit company plans to make 13.25 pound gift box of oranges and grapefruit. Each box cost $21. An orange weighs .5 pound and sells for $.75. Each grapefruit weights .75 pounds and sells for $1.25. How many oranges and grapefruit should be in each box?
:
Let x = no. of oranges
Let y - no. of grapefruits
:
Write two equations, we will use substitution here:
:
The cost equation:
.75x + 1.25y = 21
:
The weight equation:
.5x + .75y = 13.25
.5x = 13.25 - .75y
Divide the equation by .5:
x = (26.5 - 1.5y); Substitute this for x in the cost equation. find y:
;
.75(26.5-1.5y) + 1.25y = 21
19.875 - 1.125y + 1.25y = 21
.125y = 21 - 19.875
.125y = 1.125
y =
y = 9 grapefruits
:
Find x using equation .75x + 1.25y = 21
.75x + 1.25(9) = 21
.75x + 11.25 = 21
.75x = 21 - 11.25
.75x = 9.75
x =
x = 13 oranges
:
:
Check solutions in weight equation
.5x + .75y = 13.25
.5(13) + .75(9) =
6.5 + 6.75 = 13.25; confirms our solutions
:
:
Did this take some of the mystery out of this? Any questions?
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