SOLUTION: Apples cost $0.75 per pound and bananas cost $1.05 per pound. A baker bought a total of 12 pounds of apples and bananas for $10.20. The system of equations {a+b=120.75a+1.05b

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Apples cost $0.75 per pound and bananas cost $1.05 per pound. A baker bought a total of 12 pounds of apples and bananas for $10.20. The system of equations {a+b=120.75a+1.05b      Log On


   

Question 1169366: Apples cost $0.75 per pound and bananas cost $1.05 per pound.
A baker bought a total of 12 pounds of apples and bananas for $10.20.
The system of equations {a+b=120.75a+1.05b=10.20 models this situation, where a is the number of pounds of apples, and b is the number of pounds of bananas.
How many pounds of each did the baker buy?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


a%2Bb=12 [1]

.75a%2B1.05b=10.20 [2]

Use elimination: multiply the first equation by .75 and then compare the two equations (i.e., subtract one equation from the other):

.75a%2B.75b=9
.75a%2B1.05b=10.2
.3b=1.2
3b=12
b=4

ANSWER: He bought 4 pounds of bananas, which means 8 pounds of apples.

CHECK: 8($.75)+4($1.05) = $6+$4.20 = $10.20