Jacks bowling alley charges $1.50 to rent shoes and $4.50 for each game bowled. Jills bowling alley charges $2.50 to rent shoes and $4 for each game bowled. How many games must be bowled in order to make the cost of bowling at jacks the same as the cost of bowling at Jill's?

Question

Jacks bowling alley charges  $1.50 to rent shoes and $4.50 for each game bowled. Jills bowling alley charges $2.50 to rent shoes and $4 for each game bowled. How many games must be bowled in order to make the cost of bowling at jacks the same as the cost of bowling at Jill's?

phoenixfire · Answer

S=Shoes, G=Game, P=Total price
Jack: $S_{jack}=1.5$ and $G_{jack}=4.5$
Jill: $S_{jill}=2.5$ and $G_{jill}=4$

Equation per visit: $P=S+Gx$ where x is the number of games to be bowled
So we want them to be the same price $P_{jack}=P_{jill}$$$S_{jack}+G_{jack}x=S_{jill}+G_{jill}x$$Solve for x:$$S_{jack}-S_{jill}=x(G_{jill}-G_{jack})$$$${{S_{jack}-S_{jill}}\over {G_{jill}-G_{jack}}}=x={{1.5-2.5} \over {4-4.5}}={1 \over 0.5}=2$$

2 games need to be played.
$$P_{jack}=1.5+4.5(2)=10.5$$$$P_{jill}=2.5+4(2)=10.5$$

Sorry for not helping you through it. I figured after 6 hours you'd just want an answer with some explanation. Let me know if you don't understand anything.