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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have