how many pounds of candy that sells for $0.75 per lb must be mixed with candy that sells for $1.34 per lb to obtain a 7 lb mixture that sells for $0.92 per lb

Question

It needs the weight for both $0.75 candy and the$1.26 candy.

Answer 1

approximately 5 lb of $.75 mixed with 2 lbs of $1.34 yield 7 pounds of $.92

5x.75 +2x1.34 = 3.75 + 2.68 = 6.43, very close to 6.44

7x.92 = 6.44

''

solve for x = lbs of $.75

.75x + (7-x)1.34 = 7(.92)

.75x -1.34x = 7(.92)- 7(1.34)

-.59x = -7(.4) = -.42(7) = -2.94

x = 2.94/.59 = about 4.983 lbs of 75 cent

7-4.983 = about 2.017 lbs of $1.34

Answer 2

Let A = pounds of $0.75/lb candy and B = pounds of $1.34/lb candy and C = pounds of mixture A+B; then A + B = 7 pounds. Also, $0.75A + $1.34B = $0.92C, since C = 7 and using the first equation, we can substitute A=7-B into second equation:

 

0.75(7-B) + 1.34B = 0.92(7)

5.25 - 0.75B + 1.34B = 6.44

0.59B = 1.19

B = 2.0169 or 2 pounds, so 5 pounds of A plus 2 pounds of B gives 7 pounds of C @ $0.92/lb.