Question

There are 11 coins in total. Aditi!S piggy bank has $1.85. The coins are either quarters or dimes.How many of each coin are there. Solve with elimination.

Answer 1

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!