Question

Sadie has $1 worth of nickels and dimes. She has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Sadie has.

A) 5n + 10d = 1, n = 20
B) 5n + 10d = 1, d = 2n
C) 0.05n + 0.10d = 1, n = 20
D) 0.05n + 0.10d = 1, d = 2n

Answer 1

To find the number of nickels and dimes Sadie has, we use the system of equations where 0.05n + 0.10d = 1 represents the total value of coins and d = 2n represents the relationship of twice as many nickels as dimes. Option D, 0.05n + 0.10d = 1, d = 2n, is the correct system.

Step-by-step explanation:

To determine the number of nickels and dimes Sadie has, we need to set up a system of equations. Each dime is worth 10 cents, and each nickel is worth 5 cents. Since all coins combined are worth $1, we can express their total value in cents as the first equation. The second equation expresses that Sadie has twice as many nickels as dimes.

Let n represent the number of nickels and d represent the number of dimes. The correct system of equations based on the given problem is:

• 0.05n + 0.10d = 1 (This represents the total value of the coins.)
• d = 2n (This represents the relationship between the number of dimes and the number of nickels, stating that the number of dimes is half the number of nickels.)

Therefore, option D is the correct choice: 0.05n + 0.10d = 1, d = 2n.