Question

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.

Answer 1

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