To determine the number of dimes ([tex]\( d \)[/tex]) and quarters ([tex]\( q \)[/tex]) that Kyle has, we need to set up a system of equations based on the information given:
1. Kyle has a total of 30 coins. This means that the sum of the number of dimes and quarters is 30. We can write this as:
[tex]\[
d + q = 30
\][/tex]
2. The total value of the coins is [tex]\( \$4.80 \)[/tex]. Since each dime is worth [tex]\( \$0.10 \)[/tex] and each quarter is worth [tex]\( \$0.25 \)[/tex], we can express the total value of all the dimes and quarters as:
[tex]\[
0.10d + 0.25q = 4.80
\][/tex]
So, the correct system of equations that can be used to find the number of dimes ([tex]\( d \)[/tex]) and the number of quarters ([tex]\( q \)[/tex]) is:
[tex]\[
d + q = 30
\][/tex]
[tex]\[
0.10d + 0.25q = 4.80
\][/tex]
Looking at the provided options, these equations correspond to:
[tex]\[
d + q = 30
\][/tex]
[tex]\[
0.10 d + 0.25 q = 4.80
\][/tex]
Thus, the correct pair of equations from the provided options is:
[tex]\[
\boxed{d + q = 30 \text{ and } 0.10d + 0.25q = 4.80}
\][/tex]
