Question

In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has?
x + y = 16. 0.10 x + 0.25 y = 2.95.
x + y = 16. 0.05 x + 0.25 y = 2.95.
x + y = 2.95. 0.10 x + 0.25 y = 16.
x + y = 16. 0.01 x + 0.25 y = 2.95.

Answer 1

To represent the problem correctly, let's define the variables:

- Let \( x \) be the number of dimes.
- Let \( y \) be the number of quarters.

We have two pieces of information to form the equations:

1. The total number of coins (dimes and quarters) is 16:
\[
x + y = 16
\]

2. The total value of the dimes and quarters is $2.95. Since dimes are worth $0.10 and quarters are worth $0.25, we can express this as:
\[
0.10x + 0.25y = 2.95
\]

Putting these two equations together, the correct system representing the number of dimes and quarters that Hamid has is:
\[
\begin{align*}
x + y &= 16 \\
0.10x + 0.25y &= 2.95
\end{align*}
\]

Therefore, the correct option is:
**x + y = 16. 0.10 x + 0.25 y = 2.95.**