Middle School

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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 modeling this situation is:

\[ a + b = 13 \]
\[ 0.75a + 1.15b = 12.55 \]

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 :

Answer:

Step-by-step 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.

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