Question

Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase. How do you write a function rule for the cost of n sodas. How much would 10 sodas cost?

Answer 1

`c=0.75n-0.5` where `c` is your total cost in dollars and `n` is the number of sodas bought.

`10` sodas would cost `$7.00`.

Explanation:

We can start with a single formula `y=Mx+b`. This is used in the case of only one variable being changed at a constant rate (e.g. a cost per item).

`M` is your "cost per" (or slope, but in the cases of buying and selling, it means the same). Since a soda costs `$0.75`, `M` can be replaced with `0.75`.

With this information, we can say,
`y=0.75x+b`

`b` is your "base value" (it may also be referred to as a `y`-intercept). In this situation, it is not too easy to define a base value because it isn't really a base value, it's just a single change in the total outcome. Your base value is from your coupon, which takes away `$0.50` from the total cost of the purchase. Since the `$0.50` is taken away, `b` is `-0.50`. When `b` is a negative, you can subtract the value rather than add.

So now we get,
`y=0.75x-0.5`

As for the `x` and the `y`. The `y` is the outcome of the change in the `x`, and the `x` is typically what can easily be changed in the given problem. So, `x` is the number of sodas (`n`) and `y` is the total cost (`c`).

So we end up with,
`c=0.75n-0.5` where `c` is your total cost in dollars and `n` is the number of sodas bought.

Sorry if this is a bit lengthy, but I hope it helped. Cheers, and best of luck to you!