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

Algebra ->  College  -> Linear Algebra -> 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      Log On


   

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(39618) About Me  (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.
4.2%2810-x%29%2B6.9x=52.8
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

highlight_green%28R%28M-x%29%2BFx=MT%29
RM-Rx%2BFx=MT
Fx-Rx=MT-RM
%28F-R%29x=M%28T-R%29
highlight%28x=M%28%28T-R%29%2F%28F-R%29%29%29

Answer by greenestamps(13200) About Me  (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