Question

6)

solve the problem by multiplying first.
Apples cost $0.75 per pound and bananas cost $1.15 per pound. Leah bought a total of 13
pounds of apples and bananas for $12.55. The system of equations
a+b = 13
0.750 + 1.15b = 12.55 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 Leah buy?
Leah bought
pounds of apples and
pounds of bananas.

Answer 1

Explanation:

Let's solve the given system of linear equations:

a+b = 13

0.750 + 1.15b = 12.55

Let's eliminate b. To do this, solve the first equation for b, obtaining b = 13 - a, and then substitute 13 - a for b in the second equation:

0.750 + 1.15(13 - a) = 12.55.

Next, subtract 0.750 from both sides, obtaining: 1.15(13 - a) = 11.8

Dividing both sides by 1.15 yields 13 - a = 10.26

Then a = 13 - 10.26, or a = 2.74.

Since a + b = 13, b = 13 - 2.74, or 10.26

This person bought 2.74 pounds of apples and 10.26 pounds of bananas.