Question

4
A jar contains only nickels ($0.05) and dimes ($0.10).
The value of the 107 coins in the jar is $8.95. Which of
the following systems of equations, if properly solved,
would result in the correct number of nickels in the jar,
n, and the correct number of dimes in the jar, d ?

F.
n + d = 107 and 5n + 10d = 8.95
G.
n + d = 107 and 5n + 10d = 895
H.
n + d = 107 and 0.05n + 0.10d = 895
J.
n + d = 8.95 and 0.05n + 0.10d = 107
K.
n + d = 895 and 0.05n + 0.10d = 107

Answer 1

To set up the correct system of equations for this problem, we need to consider two pieces of information:

1. The total number of coins, which consists of nickels (\(n\)) and dimes (\(d\)):
\[
n + d = 107
\]

2. The total value of the coins is $8.95. Since nickels are worth $0.05 and dimes are worth $0.10, we can express the total value as:
\[
0.05n + 0.10d = 8.95
\]

Multiplying the second equation by 100 to eliminate the decimals gives:
\[
5n + 10d = 895
\]

So the system of equations is:
1. \(n + d = 107\)
2. \(5n + 10d = 895\)

Looking at the provided options, the correct system of equations is represented by:

**G.**
\[
n + d = 107 \quad \text{and} \quad 5n + 10d = 895
\]

Thus, the answer is **G**.