Question

Dan builds and sells birdhouses. The table shows his earnings.Number of Birdhouses SoldEarnings (In dollars)5401512025200?32055440Using the table, find the value of the missing numberA. 45B. 36C. 40D. 35

Answer 1

Looking at the table, the number of birdhouses sold x and the earnings y have a proportional relationship:

$y=kx$

In order to find the value of k, let's use the ordered pair (5, 40), that is, for 5 birdhouses sold, the earning is $40:

$\begin{gathered} 40=k\cdot5\\ \\ k=\frac{40}{5}=8 \end{gathered}$

Now, to find the missing value, let's use y = 320 and calculate the value of x:

$\begin{gathered} \frac{320}{x}=8\\ \\ x=\frac{320}{8}\\ \\ x=40 \end{gathered}$

The missing value is 40, therefore the correct option is C.