What would be the equations for this situation if you wanted to solve by substitution?

Question

Question 2: Mrs. Parizeau is renting out a bowling alley for a big New Years Eve tournament with her friends. She is planning on choosing from two diffeent bowling alleys to rent out for the occasion. Strike em Pins charges a flat fee of $15 for booking + $6 for every hour, per person. Murrey Bowling charges no flat fee but chares $7 for every hour, per person. Mrs. Parizeau is participating along with 6 friends. Which bowling alley should she choose?

What would be the equations? Example...
9x + 5y =3
5x + 10y =9
This kind of equation...

Answer 1

CASE 1 -- Strike em Pins ( 1 Hour)
Money to be spent = 15 + 6(6)
. = 15 + 36
. = 51 $
CASE 2 -- Murrey Bowling( 1 Hour)
Money to be spent = 7(6)
. = 42 $
So She should us ethe MURREY BOWLING.

Answer 2

Let:
x = number of hours
y = number of persons = 6

Strike Em cost = 15 + 6xy = 15 + 36x
Murrey = 7xy = 42x


You'll want to know when the cost for both alleys will be the same (i.e. at how many hours), hence:

15 + 36x = 42x
42x - 36 x = 15
6x = 15
x = 2.5 hours

Therefore, If they play for two hours, then it doesn't matter which alley she chooses.

Now based on this, find out which is cheaper if they play for less than 2.5 hours, i.e. at 1 hour:

Strike Em cost = 15 + 36(1) = 51
Murrey = 42(1) = 42

Therefore, if they play for one hour, choose Murray (cheaper); otherwise choose Strike Em.

Answer 3

Let x = total hours

36x+15 = total cost
42x = total cost

when is option A cheaper than B?

36x + 15 = 42x
x = 2.5 hours

for 2 hours or less, pick B
for 3 hours or more pick A

Answer 4

I like your question!

Strike 'em cost (c) Murrey (c)

c = 15 +6h c = 7h

Substitute c for c. In other words, set the equations equal and solve. This will be the break even point.