James has 33 coins in his pocket, all of them nickels and quarters. If he has a total of $2.25, how many quarters does he have?

spasiocuo43

spasiocuo43

Answered question

2022-11-07

James has 33 coins in his pocket, all of them nickels and quarters. If he has a total of $2.25, how many quarters does he have?

Answer & Explanation

Teagan Raymond

Teagan Raymond

Beginner2022-11-08Added 14 answers

I'm going to give nickels and quarters their own variable. Nickels will be n and quarters will be q. Since he has 33 total we can write this equation:
n+q=33

The second part is about the value of the nickels and quarters. Since nickels are worth 5 cents and quarters are worth 25 cents we can make this equation:

0.05n+0.25q=2.25

I'm actually going to multiply this whole equation by 100 to move the decimal point 2 places and make it easier to solve:

5n+25q=225

We need to find how many quarters he has, so we need to leave q in the equation so that we can solve for it. So let's rearrange the first equation:
n + q = 33 n = 33 - q

Now substitute it into the second equation:
5n+25q=225

5(33−q)+25q=225
165−5q+25q=225
165+20q=225
20q=60
q=3

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