SOLUTION: A health shop owner made trail mix containing dried fruit, nuts, and carob chips. The dried fruit sells for $5.50 per pound, the nuts sell for $7.50 per pound, and the carob chips

Algebra ->  Equations -> SOLUTION: A health shop owner made trail mix containing dried fruit, nuts, and carob chips. The dried fruit sells for $5.50 per pound, the nuts sell for $7.50 per pound, and the carob chips      Log On


   

Question 1115366: A health shop owner made trail mix containing dried fruit, nuts, and carob chips. The
dried fruit sells for $5.50 per pound, the nuts sell for $7.50 per pound, and the carob chips
sell for $8.50 per pound. The shop owner mixed 50 pounds of the trail mix and sells it for
$6.70 per pound. If the amount of nuts is five pounds more than the amount of carob ships,
how much of each item was used for the trail mix?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The dried fruit sells for $5.50 per pound, ------y pounds
the nuts sell for $7.50 per pound,--------------x+5 pounds
and the carob chips sell for $8.50 per pound.-----x pounds
The shop owner mixed 50 pounds of the trail mix
x+(x+5)+y =50
2x+y = 45............................(1)
and sells it for
$6.70 per pound.
8.50x+7.50(x+5) +5.50y = 50*6.70
16x+37.5 +5.50y = 335
16x+5.50y = 297.50
2 x + 1 y = 45 .............1


16 x + 6 y = 297.50 .............2
Eliminate y
multiply (1)by -6
Multiply (2) by 1
-12 x -6 y = -270
16 x 6 y = 298
Add the two equations
4 x = 28
/ 4
x = 7
plug value of x in (1)
2 x + 1 y = 45
14 + 1 y = 45
1 y = 31
y = 31
Ans x = 7
y = 31
carob chips 7 pounds
nuts 7+5=12 pounds
dried fruits 31 pounds