# Mary has 18 coins with a total value of $2.85. If the coins are dimes and quarters,how many of each type of coins does Mary have

[latex]x-dimes\\y-quarters\\\\ \left\{\begin{array}{ccc}x+y=18\\0,1x+0.25y=2.85&/\cdot(-10)\end{array}\right\\+\left\{\begin{array}{ccc}x+y=18\\-x-2.5y=-28.5\end{array}\right\\------------\\.\ \ \ \ \ \ -1.5y=-10.5\ \ \ \ /:(-1.5)\\.\ \ \ \ \ \ \ \ \ \ \ \ \ y=7\\\\x+7=18\\x=18-7\\x=11\\\\Answer:11\ dimes\ and\ 7\ quarters[/latex]

Let's say x represents the number of dimes and y represents the number of quarters. Note: A dime is worth 10 cents and a quarter is worth 25 cents. Therefore, their coefficients would be 0.1 and 0.25 (you must divide them by 100, since 1 dollar = 100 cents). Now you can set up a system of equations and solve by substitution. x + y = 18 0.1x + 0.25y = 2.85 In order to substitute, you have to solve for one of the variables in terms of the other. This will be easiest to do with the first equation. x + y = 18 y = 18 - x Now, substitute in that value of y into the second equation. 0.1x + 0.25(18 - x) = 2.85 Now, you can solve for x. 0.1x + 4.5 - 0.25x = 2.85 - 0.15x = -1.65 x = 11 You have 11 dimes. Now you can substitute that value into your original first equation. (11) + y = 18 y = 7 You have 7 quarters. Answer: 11 dimes and 7 quarters