SOLUTION: Mr. Charles bought a total of 5 pounds of fruit. He spent $6.58 and he bought apples, oranges, and grapes. How much of each fruit did Mr. Charles buy? Apples cost $0.95/pound

Question 1012192: Mr. Charles bought a total of 5 pounds of fruit. He spent $6.58 and he bought apples, oranges, and grapes. How much of each fruit did Mr. Charles buy?
Apples cost $0.95/pound
Oranges cost $0.83/pound
grapes cost 1.60/pound
Thank you for your consideration of assistance.

Found 2 solutions by ikleyn, macston:
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
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Mr. Charles bought a total of 5 pounds of fruit. He spent $6.58 and he bought apples, oranges, and grapes. How much of each fruit did Mr. Charles buy?
Apples cost $0.95/pound
Oranges cost $0.83/pound
grapes cost 1.60/pound
Thank you for your consideration of assistance.

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Let x = amount of apples bought (in pounds), y = amount of oranges bought (in pounds), z = amount of grapes bought (in pounds). Then you have two equations for three unknowns x, y and z: x + y + z = 5, 0.95x + 0.83y + 1.60z = 6.58. This information is not sufficient to solve the system. The additional information is required.

The other tutor solved the problem assuming that the amount for each fruit is the whole number of pounds.

This assumption did not contain in the original formulation.

It is that additional info/assumption I talked about in my solution.

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
A=pounds of apples; R=pounds of oranges; G=pounds of grapes
.
The problem indicates he bought all three, so he must
have bought at least 1 pound of each:
.
$0.95+$0.83+$1.60=$3.38
.
He has bought 3 pounds and spent $3.38, so he has
2 more pounds to buy and ($6.58-$3.38=) $3.20 to spend.
The only combination of two pounds that adds up to $3.20
is two ponds of grapes.
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ANSWER: Mr. Charles bought one pound of apples,
one pound of oranges, and three pounds of grapes.
.
CHECK:
$0.95A+$0.83R+$1.60G=$6.58
$0.95(1)+$0.83(1)+&1.60(3)=$6.58
$0.95+$0.83+$4.80=$6.58
$6.58=$6.58
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