Scarlett has 13 coins worth $2.95. if the coins are all quarters and dimes, how many does she have in total?

She has 11 quarters and 2 dimes.

Step-by-step explanation:

Let the amount of quarters = q

And the amount of dimes = d

We can write 2 equations with the given information.

q + d = 13 --- amount of quarters plus amount of dimes = 13 coins

0.1d + 0.25q = 2.95 --- a time is 0.1 dollars and a quarter is 0.25 dollars each

Now we can solve for both values as a system of equations.

q + d = 13

q = 13 - d --- subtract d from both sides to get q by itself

0.1d + 0.25(13 - d) = 2.95 --- substitute in our new value for q into the other equation so we only have 1 variable

0.1d + 3.25 - 0.25d = 2.95 --- distribute 0.25

-0.15d + 3.25 = 2.95 --- combine like terms

-0.15d = -0.3 --- subtract 3.25 from both sides

d = 2 --- divide both sides by -0.15

Now we can go back to the first equation because we know what d is.

q + 2 = 13

q = 11 --- subtract 2 from both sides.

She has 11 quarters and 2 dimes.

0.1d + 0.25q = 2.95

0.1(2) + 0.25(11)

0.2 + 2.75

2.95 = 2.95

Answer is correct.

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step-by-step explanation:

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