Answer:
$3.2
Step-by-step explanation:
Let x be the cost of each cupcake and y be the cost of each slice of pie.
We have been given that the cost of one cupcake and two slices of pie is $12.40. We can represent this information as:
[tex]x+2y=12.40...(1)[/tex]
We have been given that the cost of two cupcakes and three slices of pie is $20.20. We can represent this information as:
[tex]2x+3y=20.20...(2)[/tex]
We will use substitution method to solve for the cost of one cupcake.
From equation (1) we will get,
[tex]y=\frac{12.40-x}{2}[/tex]
Substituting this value in equation (2) we will get,
[tex]2x+3(\frac{12.40-x}{2})=20.20[/tex]
[tex]\frac{4x}{2}+3(\frac{12.40-x}{2})=20.20[/tex]
[tex]\frac{4x}{2}+\frac{37.2-3x}{2}=20.20[/tex]
[tex]\frac{4x+37.2-3x}{2}=20.20[/tex]
[tex]2\times \frac{4x+37.2-3x}{2}=2\times 20.20[/tex]
[tex]4x+37.2-3x=40.40[/tex]
[tex]4x+37.2-37.2-3x=40.40-37.2[/tex]
[tex]4x-3x=40.40-37.2[/tex]
[tex]x=3.2[/tex]
Therefore, cost of one cupcake is $3.2.
