Question

Mark has 4 more dimes than quarters in his pocket. In total he has $3.10. Which equation could be used to determine the number of dimes, x, in his pocket?

a) 0.25x + 0.10(x + 4) = 3.10
b) 0.25x - 0.10(x + 4) = 3.10
c) 0.10x - 0.25(x + 4) = 3.10
d) 0.10x + 0.25(x + 4) = 3.10

Answer 1

The correct equation to represent the total amount of money Mark has, given he has 4 more dimes than quarters and a total of $3.10, is 0.10x + 0.25(x - 4) = 3.10. Option (a) is most similar, but requires a correction from (x + 4) to (x - 4).

Step-by-step explanation:

The student is trying to find out the number of dimes, x, in Mark's pocket given that he has 4 more dimes than quarters and a total amount of $3.10. The value of a dime is $0.10, and the value of a quarter is $0.25.

To set up the equation, let's consider the quarters. If x represents the number of dimes, then Mark would have x - 4 quarters because he has 4 more dimes than quarters. To find the total value, we multiply the number of each type of coin by their respective values and set the equation equal to the total amount of $3.10.

The correct equation, therefore, is:

0.10x + 0.25(x - 4) = 3.10

This equation represents the value of the dimes (0.10x) plus the value of the quarters (0.25 times the number of quarters, which is x - 4), equal to the total amount of $3.10. Option (a) is closest to the correct formula, but with a slight adjustment - replacing (x + 4) with (x - 4).