Question

Find the missing digit and check calculations.went to the store and bought 18 two-litter bottles of off-brand soda for his Super Bowl party last weekend. His receipt is smuggled, But he can see that the cost of these bottles before tax was 15.#4. how much did each bottle cost?

Answer 1

We have a smuggled total that is 15.#4 after buying 18 bottles.

We can estimate the cost of each bottle as:

`p=(15+0.1\cdot x+0.04)/(18)`

where x is the tenths of a dollar, and it will have an integer value between 0 and 9.

If we try the different possible values for x, we get:

`\begin{gathered} x=0\Rightarrow15.04/18=0.835555555555555 \\ x=1\Rightarrow15.14/18=0.841111111111111 \\ x=2\Rightarrow15.24/18=0.846666666666667 \\ x=3\Rightarrow15.34/18=0.852222222222222 \\ x=4\Rightarrow15.44/18=0.857777777777778 \\ x=5\Rightarrow15.54/18=0.863333333333333 \\ x=6\Rightarrow15.64/18=0.868888888888889 \\ x=7\Rightarrow15.74/18=0.874444444444444 \\ x=8\Rightarrow15.84/18=0.88 \\ x=9\Rightarrow15.94/18=0.885555555555556 \end{gathered}`

We can see that the only value that give a unit price in cents is for x = 8, which corresponds to a total price of $15.84 and a unit price of $0.88.

Answer: we can estimate that the unit price is $0.88.