SOLUTION: Raisins worth $4.20/kg are mixed with dried fruit worth $6.90/kg to make a mixture worth $5.28/kg. How many kilograms of dried fruit must be used to make 10 kg of the mixture. t

Question 1161277: Raisins worth $4.20/kg are mixed with dried fruit worth $6.90/kg to make a mixture worth $5.28/kg. How many kilograms of dried fruit must be used to make 10 kg of the mixture.
thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!

PRICE MASS COST raisins 4.2 10-x 4.2(10-x) dried fruit 6.9 x 6.9x MIXTURE 5.28 10 5.28*10

Equate the costs.

Simplify and solve for x.

-----------All In Variables Only---------------
KNOWN VARIABLES, GIVEN: R, F, T, M
UNKNOWN VARIABLE: x

PRICE MASS COST raisins R M-x R(M-x) dried fruit F x Fx MIXTURE T M MT

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A non-algebraic solution method....

(1) find where the price per pound of the mixture lies between the cost of the raisins and the cost of the dried fruit.

On a number line, 5.28 is 2/5 of the way from 4.20 to 6.90:

4.20 to 6.90 is a difference of 2.70
4/20 to 5.28 is a difference of 1.08
1.08/2.70 = 2/5

(2) That fraction is the fraction of the mixture that needs to be the more expensive ingredient.

ANSWER: 2/5 of 10 pounds, or 4 pounds, of the dried fruit; the other 6 pounds is raisins.

CHECK:
4(6.90)+6(4.20) = 27.60+25.20 = 52.80
10(5.28) = 52.80

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