Solving Systems by Elimination (Multiply)

Question

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=12

                                          0.75a+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 1

.75a +1.05b ==10.20

Clearing the decimals,

75a +105b=1020

factor by 5

15a +21b =204

a+b = 12

multiply above by (-15)

15a + 21b =204

-15a -15b =-140

Adding and eliminating,

6b= 64, b=10.7 lbs.

a=1.3 lbs.

Answer 2

.75a+1.05b=12

Without any more imfo; there's more than 1 answer.

Think of the weight; each piece isn't going to be a whole pound.