Question

Joel and Kevin are each putting money in a savings account to buy a new bicycle. The amount, in dollars, in Joel’s savings account, x weeks after the start of the year, is modeled by function j. The amount of money in Kevin’s account, at the same time, is modeled by function k.
j(x) = 25 + 3x
k(x) = 15 + 2x

Which function correctly represents how much more money, in dollars, is in Joel’s account than in Kevin’s account x weeks after the start of the year?

A.
(j − k)(x) = 40 + 5x
B.
(j − k)(x) = 40 + x
C.
(j − k)(x) = 10 + 5x
D.
(j − k)(x) = 10 + x

Answer 1

Given:

The amount of money in Joel’s account is:

$j(x)=25+3x$

The amount of money in Kevin’s account is:

$k(x)=15+2x$

To find:

The function that correctly represents how much more money, in dollars, is in Joel’s account than in Kevin’s account x weeks after the start of the year.

Solution:

We need to find the difference between the function j(x) and function k(x).

$j(x)-k(x)=(25+3x)-(15+2x)$

$(j-k)(x)=25+3x-15-2x$

$(j-k)(x)=(25-15)+(3x-2x)$

$(j-k)(x)=10+x$

Therefore, the correct option is D.