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For Monday morning's staff meeting, Jim bought 3 bags of bagels and 3 packages of cream cheese and paid $16.50 (excluding sales tax).For Friday's meeting, he bought 5 bags of bagels and 2 packages of cream cheese and paid $22.25 (again, excluding sales tax). How much dobags of bagels and packages of cream cheese cost?

For Monday morning's staff meeting, Jim bought 3 bags of bagels and 3 packages of-example-1
For Monday morning's staff meeting, Jim bought 3 bags of bagels and 3 packages of-example-1
For Monday morning's staff meeting, Jim bought 3 bags of bagels and 3 packages of-example-2
User Vijay Sali
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1 Answer

1 vote

Answer:

Explanation:

Let the price of one bag of bagel = b

Let the price of one package of cream cheese = c

3 bags of bagels and 3 packages of cream cheese costs $16.50.


3b+3c=16.50\cdots(1)

5 bags of bagels and 2 packages of cream cheese costs $22.25.


5b+2c=22.25\cdots(2)

Thus, we derive a system of two linear equations which we then solve for b and c.


\begin{gathered} 3b+3c=16.50\operatorname{\cdots}(1) \\ 5b+2c=22.25\operatorname{\cdots}(2) \end{gathered}

Multiply equation 1 by 5 and equation 2 by 3.


\begin{gathered} 15b+15c=82.5 \\ 15b+6c=66.75 \end{gathered}

Subtract to eliminate b.


9c=15.75

Divide both sides by 9:


\begin{gathered} (9c)/(9)=(15.75)/(9) \\ c=1.75 \end{gathered}

Next, substitute c=1.75 into equation 1.


\begin{gathered} 3b+3c=16.50 \\ 3b+3(1.75)=16.50 \\ 3b=16.50-3(1.75)=11.25 \\ b=(11.25)/(3)=3.75 \end{gathered}

The price per bag of bagel is $3.75 and the price per package of cream cheese is $1.75.

User KimHee
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