Question

Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 6 tiles the firstday. She started to go faster and by the end of day 4, she had placed 36 tiles. She worked at a steady rateafter the first day. Use an equation in point-slope form to determine how many days Lizzy took to placeall of the 100 tiles needed to finish the floor. Solve the problem using an equation in point-slope form.

Answer 1

We know that

• She placed 6 tiles on the first day.

,

• By the end of day 4, she had placed 36 tiles.

Based on the given information, we can express the following equation.

`y=3x+6`

If she had placed 36 tiles in 3 days, it means she had placed 12 tiles per day, that's why the coefficient of x is 3. And the number 6 is the initial condition of the problem, that is, on day 0 she placed 6 tiles.

Now, for 100 tiles, we have to solve the equation when y = 100.

`\begin{gathered} 100=3x+6 \\ 100-6=3x \\ 3x=94 \\ x=(94)/(3) \\ x=31.33333\ldots \end{gathered}`

Therefore, she needs 32 days to place all the tiles.

Notice that we cannot say 31 days, because it would be incomplete.