Question

Michelle has 43 coins of change in her pocket made up of nickels (n), dimes (d), and quarters (q). She has three times as many quarters than she has dimes. The total value of her change is $6.70. Which system of equations below can be solved to find the exact number of nickels, dimes, and quarters in Michelle’s pocket?

a) 5n + 10d + 25q = 670
b) n + d + q = 43
c) q = 3d
d) n + 2d + 4q = 70

Answer 1

The system of equations that can be solved to find the exact number of nickels, dimes, and quarters in Michelle’s pocket are: 5n + 10d + 25q = 670, n + d + q = 43, and q = 3d.

Step-by-step explanation:

The system of equations that can be solved to find the exact number of nickels, dimes, and quarters in Michelle’s pocket is:

a) 5n + 10d + 25q = 670

b) n + d + q = 43

c) q = 3d

The equation a represents the total value of Michelle's change, where the value of each nickel is 5 cents (5n), the value of each dime is 10 cents (10d), and the value of each quarter is 25 cents (25q). The equation b represents the total number of coins in Michelle's pocket. The equation c represents the relationship between the number of quarters and the number of dimes.