Question

Rodrigo has a total of 10 coins in dimes and quarters (D + Q = 10), and the number of dimes is four times the number of quarters (D = 4Q). How many dimes and how many quarters does Rodrigo have?

a. 2 dimes, 8 quarters
b. 3 dimes, 7 quarters
c. 4 dimes, 6 quarters
d. 5 dimes, 5 quarters

Answer 1

Rodrigo has a total of 2 quarters and 8 dimes, which is found by solving a system of equations that represents the constraints on the number of his coins.

Step-by-step explanation:

To determine how many dimes and quarters Rodrigo has, we can set up a system of equations based on the given information. We know that Rodrigo has a total of 10 coins consisting of dimes and quarters, which gives us our first equation: D + Q = 10. Furthermore, we are told that the number of dimes is four times the number of quarters, giving us our second equation: D = 4Q.

Let's solve the system of equations step-by-step:

1. Start with the two equations:
   
2. Substitute Equation 2 into Equation 1:
   
3. Divide both sides by 5:
   
4. Use the value of Q to find D:
   

Therefore, Rodrigo has 2 quarters and 8 dimes. This corresponds to option (a): 2 dimes and 8 quarters.