Maggie has only dimes and quarters in her purse. she has 27 coins with a total value of 4.05. how many dimes does maggie have in her purse

By solving a system of equations, we will see that Maggie has 18 dimes and 9 quarters.

First, we define the variables that we will use:

There are a total of 27 coins, so:

Q + D = 27.

The total value is 4.05, so:

Q*0.25 + D*0.10 = 4.05

Then our system of equations:

Q + D = 27

Q*0.25 + D*0.10 = 4.05

To solve this we need to isolate one of the variables in one of the equations, I will isolate Q in the first one.

Q = 27 - D

Now we can replace this on the other equation and solve it for D:

(27 - D)*0.25 + D*0.10 = 4.05

6.75 - D*0.25 + D*0.10 = 4.05

6.75 - D*0.15 = 4.05

6.75 - 4.05 = D*0.15

2.70 = D*0.15

2.70/0.15 = D = 18

So she has 18 dimes, and then the other 9 conis must be quarters.

If you want to learn more about systems of equations, you can read:

link

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step-by-step explanation:

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