Answer:
[tex]15[/tex] quarters and [tex]3[/tex] dimes.
Step-by-step explanation:
In this question, it is given that a total of [tex]18[/tex] quarters ([tex]0.25[/tex] dollars each) and dimes ([tex]0.10[/tex] dollars each) add up to a value of [tex]4.05[/tex] dollars. The goal is to find the number of each type of coins.
Let [tex]x[/tex] denote the number of quarters. There would be [tex](18 - x)[/tex] dimes since there were a total of [tex]18[/tex] coins. The total value of the coins is [tex]4.05[/tex], meaning that:
[tex](0.25)\, x + (0.1)\, (18 - x) = 4.05[/tex].
Rearrange this equation and solve for [tex]x[/tex]:
[tex]0.15\, x = 2.25[/tex].
[tex]x = 15[/tex].
In other words, there would be [tex]15[/tex] quarters and [tex](18 - 15) = 3[/tex] dimes.
