Q8. - Algebra 1

Question

The linear equation below is a best fit model for the peak depth of the Mad River when $x$ inches of rain fall. What would you expect the peak depth of the river to be after a storm that produces $1\frac{3}{4}$ inches of rain? Round your answer to the nearest tenth of a foot if necessary.

$y=2.5x+14.8$

Step-by-Step Solution

Answer

The peak depth of the river after a storm that produces $1\frac{3}{4}$ inches of rain is $1.6$ feet.

Step 1. Write the equation that models the relationship between the peak depth ( y ) of river and x inches of rain.

The equation that models the relationship between the peak depth ($y$) of river and $x$ inches of rain is:

$y=2.5x+14.8$

Step 2. Find the peak depth of the river after a storm that produces 1 3 4 inches of rain.

The peak depth of the river after a storm that produces $1\frac{3}{4}$ inches of rain can be find out be substituting $1\frac{3}{4}$ for $x$ in the equation $y=2.5x+14.8$.

Therefore, it is obtained that:

$$\begin{gathered} y=2.5\left(1\frac{3}{4}\right)+14.8 \\ =2.5\left(\frac{7}{4}\right)+14.8 \\ =2.5\left(1.75\right)+14.8 \\ =4.375+14.8 \\ =19.175 \end{gathered}$$

Therefore, the peak depth of the river is $19.175$ inches.

Find the peak depth of the river in feet.

$\begin{array}{c}19.175\text{ inches}=\frac{19.175}{12}\text{feet }\left(\because 1\text{ foot}=12\text{ inches}\right)\\ =1.5979167\text{ feet}\end{array}$

Therefore, the peak depth of the river after rounding to the nearest tenth of a foot is $1.6$ feet.

Therefore, the peak depth of the river after a storm that produces $1\frac{3}{4}$ inches of rain is $1.6$ feet.