Question

a book store manager observes that the number of magazines sold seems to vary inversely as the price per magazine. if the store sells 380 magazines per week when the price per magazine is $5.30, how many does he expect to sell if he lowers the price to $4? round your answer to the nearest integer if necessary.

Explanation:

Step1: Recall inverse - variation formula

Let $n$ be the number of magazines sold and $p$ be the price per magazine. The inverse - variation formula is $n_1p_1=n_2p_2$.

Step2: Identify given values

We know that $n_1 = 380$, $p_1=5.30$, and $p_2 = 4$.

Step3: Solve for $n_2$

Substitute the values into the formula: $380\times5.30=n_2\times4$. Then $n_2=\frac{380\times5.30}{4}$.
First, calculate $380\times5.30 = 380\times(5 + 0.3)=380\times5+380\times0.3=1900+114 = 2014$.
Then, $n_2=\frac{2014}{4}=503.5$.

Answer:

504