[tex] \\ \text{Let the number of dimes be D and number of quarters be Q.}\\ \\ \text{Since Jason has total 17 coins, so }\\ \\ D+Q=17 \ \ \ \ \ \ \ \ \ ...... (i)\\ \\ \text{and total he has }\$ 2.90, \text{ so we have}\\ \\ 0.10 D+0.25Q=2.90 \ \ \ \ \ \ \ ...... (ii)\\ [/tex]
[tex] \\ \text{Now from equation (i), substitute, }D=(17-Q) \text{ in equation (ii)}.\\ \text{so we get}\\ \\ 0.10 (17-Q)+0.25Q=2.90\\ \\ \Rightarrow 1.7-0.10Q+0.25Q=2.90\\ \\ \Rightarrow 1.7+0.15Q=2.90\\ \\ \Rightarrow 0.15Q=2.90-1.7\\ \\ \Rightarrow 0.15Q=1.20\\ \\ \Rightarrow Q=\frac{1.20}{0.15}\\ \\ \Rightarrow Q=8\\ \\ \text{subsitute back this value of Q in (i), we get} \\ \\ D=17-8=9\\ [/tex]
Hence number of dimes =9
And number of quarters=8
