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

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

Answered by iloveonedirection | 2024-06-10

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

Answered by Anonymous | 2024-06-10

Mary has 11 dimes and 7 quarters. We derived this by setting up two equations based on the total number of coins and their total value. By solving the equations step-by-step, we found the quantities of each type of coin.
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Answered by iloveonedirection | 2024-12-19