Question

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?

Answer 1

$27.75

Explanation:

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`