Answer:
Caleb and Devon each bowled for [tex]10[/tex] hours and spent [tex]\$55[/tex].
Step-by-step explanation:
Equations:
- Caleb: y = 4x + 15
- Devon: y = 5x + 5
Where:
- x = hours spent bowling
- y = the total cost
System of equations:
[tex]\begin{cases}y=4x+15\\y=5x+5\end{cases}[/tex]
Solve for x
Step 1: Substitute the second equation into the first.
[tex]\implies 4x+15=5x+5[/tex]
Step 2: Subtract [tex]5x[/tex] from both sides
[tex]\implies 4x-5x+15=5x-5x+5[/tex]
[tex]\implies -x+15=5[/tex]
Step 3: Subtract [tex]15[/tex] from both sides.
[tex]\implies -x+15-15=5-15[/tex]
[tex]\implies -1x=-10[/tex]
Step 4: Divide both sides by [tex]-1[/tex] .
[tex]\implies \dfrac{-1x}{-1}=\dfrac{-10}{-1}[/tex]
[tex]\implies \boxed{x=10}[/tex]
Solve for y
Step 1: Substitute the found [tex]x[/tex] value into one of the system of equations.
[tex]\implies y=4(10)+15[/tex]
Step 2: Multiply and add.
[tex]\implies y=40+15[/tex]
[tex]\implies \boxed{y=55}[/tex]
Therefore, Caleb and Devon each bowled for 10 hours and spent $55.
