SOLUTION: One type of candy sells for $2 per pound and another type sells for $3 per pound. An order for 18 pounds costs $47. How much of each type of candy was purchased?

Question 938682: One type of candy sells for $2 per pound and another type sells for $3 per pound. An order for 18 pounds costs $47. How much of each type of candy was purchased?

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Given:
Type A candy = $2 / lb
Type B candy = $3 / lb
18 pounds total cost $47.

Solution method 1: using system of two equations,
================================================
A,B = respective weight of each candy purchased in pounds.
A+B=18....(1)
2A+3B=47....(2)

Solve by substitution
A=18-B....(1a)

substitute (1a) in (2)
2(18-B)+3B=47....(3)

Solve for B
36-2B+3B=47
B=47-36=11....(4)

substitute (4) into (1a)
A=18-B=18-11=7

Answer: 7 lbs of A and 11 lbs of B were purchased.

Check: 7*2+11*3=$47, ok.

Method 2: mental reasoning
==========================
Given:
Type A candy = $2 / lb
Type B candy = $3 / lb
18 pounds total cost $47.
step 1: If all 18 lbs were type A, it would have cost $2*18=$36
step 2: There is an excess cost of $47-$36 = $11,
so number of pounds of type B purchased = $11/($3-$2)=11 lbs
step 3: weight of type A purchased = 18-11=7 lbs.
Answer: 7 lbs of A and 11 lbs of B.
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