[tex] \text{Suppose you have x quarters, (3x+2) dimes, (5x+1) nickels and (6x+4) pennies}\\ \text{and total value of the coins is }\$ 4.59\\ \\ \text{we know that the value of 1 quarter is}=\$ 0.25\\ \\ \text{value of 1 dime}=\$0.10\\ \\ \text{value of 1 Nickel}=\$ 0.05\\ \\ \text{value of 1 Penny}=\$ 0.01\\ \\ \text{so the equation that represents the given situation is} [/tex]
0.25 x+0.10(3x+2)+0.05(5x+1)+0.01(6x+4)=4.59
[tex] \\ \text{now to find the number of each coin, we solve it. so}\\ \\ 0.25 x+0.3x+0.20+0.25x+0.05+0.06x+0.04=4.59\\ \\ 0.86x+0.29=4.59\\ \\ \Rightarrow 0.86x=4.59-0.29\\ \\ \Rightarrow 0.86x=4.3\\ \\ \Rightarrow x=\frac{4.3}{0.86}\\ \\ \Rightarrow x=5 [/tex]
So the number of quarters is: 5
Number of dimes=3x+2=3(5)+2=17
Number of nickels=5x+1=5(5)+1=26
And number of Pennies=6x+4=6(5)+4=34
