Solve.
-A vendor has learned that, by pricing carmel apples at $\$ 1.25$, sales will reach 91 carmel apples per day. Raising the price to $\$ 2.25$ will cause the sales to fall to 43 carmel apples per day. Let $y$ be the number of carmel apples the vendor sells at $x$ dollars each. Write a linear equation that relates the number sold $y$ to the price $x$.
A) $y = - 48 x - 151$
B) $y = 48 x + 31$
C) $y = - 48 x + 151$
D) $y = - \frac { 1 } { 48 } x + \frac { 17467 } { 192 }$

Question

Quizplus · Accepted Answer

The relationship between the price $x$ and the number of carmel apples sold $y$ is linear, and we can use the two given points to find the slope: $\frac{43 - 91}{2.25 - 1.25} = -48$. Then, using one of the points, say $x = 1.25, y = 91$, we can find the y-intercept: $91 = -48(1.25) + b$, solving for $b$ gives $b = 151$. Thus, the equation is $y = -48x + 151$.

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-A Vendor Has Learned That, by Pricing Carmel Apples $\$ 1.25$