Answer:
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
