Hey there! I'm happy to help!
Let's represent our number of quarters with q and our dimes with d. We know that each q has a value of 0.25, and each d has a value of 0.1. This means that 0.25q+0.1d=1.85. We also know that q+d=11 as there are 11 total coins.
Here is our system of equations.
0.25q+0.1d=1.85
q+d=11
We are asked to solve with elimination. To do this, we need combine the equations to cancel out a variable to solve for the other. We have 1d on the bottom. Let's multiply the entire top equation by -10 to get a -1d on the top so we can do this.
-2.5q-d=-18.5
q+d=11
We combine the equations.
-1.5q=-7.5
We divide both sides by -1.5
q=5
Since there are 11 coins in total, this means that there are 5 quarters and 6 dimes.
Have a wonderful day!
