How many pounds of nuts selling for
$18
per lb and raisins selling for
$6
per lb should a person combine to obtain 90
lb of a trail mix selling for
$10
per lb?
The person would need __
lb of nuts selling for
$18
and ___lb of raisins selling for
$6.
This is the concept of simultaneous equation; Suppose x lb of nuts and y lb of raisins to obtain the required amount; to solve the expression we proceed as follows; Total price should give us 90 lb, thus; x+y=90.......i The final price should give us $10, thus; 18x+6y=10*90 simplifying this we get; 9x+3y=5.....ii Solving the equations by substitution; From i we get: x+y=90 x=90-y.....iii substitute iii in ii we get: 9x+3y=5 18(90-y)+6y=900 opening the brackets we get: 1620-18y+6y=900 collecting the like terms we get: -12y=-720 -12y=-720 thus y=(-720)/(-12) y=60
Thus x=90-60=30 the answer is 30 lb nuts were 60 lb of raisins were used
