Question

Select the correct answer.

Pat and Quentin collect trading cards. They each began the year with cards already in their collection and bought more cards every month. The number of cards in Par's collection, x months after the start of the year, is modeled by function p p(x) = 34 + 16x The number of cards in Quentin's collection, x months after the start of the year, is modeled by function g phi(x) = 28 + 12x
Which function correctly represents how many more cards Pat has in her collection than Quentin has in his collection, x months after the start of the year?
A (p - q)(x) = 6 + 4x.
B. (p - q)(x) = 62 + 28x
C. (p - q)(x) = 6 + 28x
D. (p - q)(x) = 62 + 4x​

Answer 1

To find the function representing how many more cards Pat has than Quentin after x months, subtract Quentin's function from Pat's. The result is (p - q)(x) = 6 + 4x, which corresponds to option A.

Step-by-step explanation:

The question is asking to find the function that represents how many more cards Pat has in her collection than Quentin, x months after the start of the year. To find this, we take the function for Pat's collection, p(x) = 34 + 16x, and subtract the function for Quentin's collection g(x) = 28 + 12x. Performing the subtraction, we get:

(p - g)(x) = p(x) - g(x) = (34 + 16x) - (28 + 12x)

By simplifying the right-hand side of the equation, we combine like terms:

(p - g)(x) = (34 - 28) + (16x - 12x) = 6 + 4x

Therefore, the correct answer is A. (p - q)(x) = 6 + 4x.