A bowling alley offers special weekly bowling rates. The weekly rates are 5 games for $15, 6 games for $17.55, 7 games for $20.10, and 8 games for $22.65. lf this pattern continues, how much will it cost to bowl 10 games in a week?

Question

Nathan Axel · Accepted Answer

$27.75

The thing to do is experiment with ideas that associate the numbers looking for a pattern of behaviour. Eventually you should find something that works.

Lets try dividing cost by count

#("cost")/("game count")-> 15/5, 17.55/6, 20.1/7, 22.65/8#
#" "darr" "darr" "darr" "darr#
#" " 3", "2.19..", "2.87..", "2.83..#

NOTHING AMEDIATELY OBVIOUS!
Actually there is something hear but it is hidden.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lets try rate of change.

Set #"x-axis "->" the set of numbers "{5,6,7,8}#

Set #"y-axis "->" the set of numbers "{15", "17.55", "20.1", "22.65}#

1st pair to 2nd pair:
#" change in x is 1"#
#" change in y is "17.55-15=2.55#

2nd pair to 3rd pair:
#" change in x is 1"#
#" change in y is "20.1-17.55=2.55#

3rd pair to 4th pair:
#" change in x is 1"#
#" change in y is "22.65-20.1=2.55#

#color(red)("Found a consistent relationship") #
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the same thing as a straight line graph

For each increase in x by 1 the y increases by 2.55

So 2.55 is the value of #m# in the equation: #y=mx+c# giving:

#y=2.55x+c#

Picking on any pair; I select #(x,y)=(5,15)#

Then #y=2.55x+c" "->" "15=2.55(5)+c#

#c=2.25# giving

#y=2.55x+2.25# where #x# is the number of games and #y# is the cost.

We need 10 games so #" "y=2.55(10)+2.25" " =" " $27.75#

Ethan Adkins · Answer

undefined To determine the cost of bowling 10 games in a week using the pattern provided, we can use the relationship between the number of games and the cost. The pattern suggests that for each additional game, the cost increases by $2.55.

Starting with the given rates:
5 games cost $15,
6 games cost $17.55,
7 games cost $20.10,
8 games cost $22.65.

From this pattern, we can observe that for each additional game, the cost increases by $2.55.

So, for 9 games, the cost would be $22.65 + $2.55 = $25.20.

And for 10 games, the cost would be $25.20 + $2.55 = $27.75.

Therefore, it would cost $27.75 to bowl 10 games in a week using this pattern.