Answer:
48 dimes
Step-by-step explanation:
To determine how many dimes are in the jar, we can create and solve a system of equations.
Let n be the number of nickels in the jar.
Let d be the number of dimes in the jar.
Given that there are a total of 60 coins in the jar, this can be expressed as:
[tex]n + d = 60[/tex]
A nickel has the value of $0.05, and a dime has the value of $0.10. Given that the total value of the coins is $5.40, then:
[tex]0.05n + 0.10d = 5.40[/tex]
Therefore, the system of equations that represents the given scenario is:
[tex]\begin{cases} n + d = 60\\0.05n + 0.10d = 5.40\end{cases}[/tex]
To solve, rearrange the first equation to isolate n:
[tex]n = 60 - d[/tex]
Now, substitute this into the second equation and solve for d:
[tex]0.05(60-d)+0.10d=5.40 \\\\ 0.05(60-d)+0.10d=5.40 \\\\ 3-0.05d+0.10d=5.40 \\\\ 3+0.05d=5.40 \\\\ 0.05d = 5.40 - 3 \\\\ 0.05d = 2.40 \\\\ d=\dfrac{2.40}{0.05} \\\\ d=48[/tex]
Therefore, the number of dimes in the jar is:
[tex]\LARGE\boxed{\boxed{ \sf 48 \; dimes}}[/tex]
