Question

Jackson has a coin collection consisting of quarters and dimes. The total

value of his collection is $15.05. His collection consists of seven less
quarters than two times the number of dimes. Using the variables q and d
to represent the number of quarters in his collection and the number of
dimes in his collection respectively, determine a system of equations that
describes the situation.

Answer 1

The system of equations for Jackson's coin collection is 0.25q + 0.10d = 15.05 (representing the total value) and q = 2d - 7 (representing the relationship between the number of quarters and dimes).

Step-by-step explanation:

To find a system of equations for Jackson's coin collection problem, we need to translate the given information into two equations using the variables q for the number of quarters and d for the number of dimes.

First, the total value of quarters and dimes equals $15.05. Since each quarter is worth $0.25 and each dime is worth $0.10, we can write the total value equation as:

0.25q + 0.10d = 15.05

Next, the problem states Jackson has seven less quarters than two times the number of dimes. This gives us the second equation which relates the number of quarters to the number of dimes:

q = 2d - 7

Therefore, the system of equations that describe Jackson's coin collection is:

• 0.25q + 0.10d = 15.05
• q = 2d - 7