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.
[tex]3b+3c=16.50\cdots(1)[/tex]5 bags of bagels and 2 packages of cream cheese costs $22.25.
[tex]5b+2c=22.25\cdots(2)[/tex]Thus, we derive a system of two linear equations which we then solve for b and c.
[tex]\begin{gathered} 3b+3c=16.50\operatorname{\cdots}(1) \\ 5b+2c=22.25\operatorname{\cdots}(2) \end{gathered}[/tex]Multiply equation 1 by 5 and equation 2 by 3.
[tex]\begin{gathered} 15b+15c=82.5 \\ 15b+6c=66.75 \end{gathered}[/tex]Subtract to eliminate b.
[tex]9c=15.75[/tex]Divide both sides by 9:
[tex]\begin{gathered} \frac{9c}{9}=\frac{15.75}{9} \\ c=1.75 \end{gathered}[/tex]Next, substitute c=1.75 into equation 1.
[tex]\begin{gathered} 3b+3c=16.50 \\ 3b+3(1.75)=16.50 \\ 3b=16.50-3(1.75)=11.25 \\ b=\frac{11.25}{3}=3.75 \end{gathered}[/tex]The price per bag of bagel is $3.75 and the price per package of cream cheese is $1.75.