Question

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?

Answer 1

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.

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.