Brianna has $2.80 in quarters, dimes and nickels in her purse. She has nine more dimes than quarters and six more nickels than quarters. How many of each coin does she have?

She has 4 quarters, 13 dimes, and 10 nickels in her purse

Step-by-step explanation:

Let q be the amount of quarters, d be the amount of dimes, and n be the amount of nickels she has in her purse. We can use this to set up a system of equations:

25q+10d+5n=280

This is because a quarter is 25 cents, a dime is 10 cents, and a nickel is 5 cents. We also have to convert $2.80 to cents since all our other values are in cents.

d=q+9

She has 9 more dimes than quarters

n=q+6

She has 6 more nickels than quarters

We can solve this system using substitution (substitute q+9 for d and q+6 for n)

25q+10(q+9)+5(q+6)=280

25q+10(q)+10(9)+5(q)+5(6)=280

25q+10q+90+5q+30=280

40q+120=280

Subtract 120 from both sides

40q=160

Divide both sides by 40

q=4

Now we plug this back into the other equations to find the amount of nickels and dimes

d=q+9=4+9=13

n=q+6=4+6=10

She has 4 quarters, 13 dimes, and 10 nickels in her purse

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