At the end of her shift a cashier has a total of $6.30 in dimes and quarters. there are 7 more dimes than quarters. how many of each of these coins does she have?

The cashier has 23 dimes and 16 quarters.

Step-by-step explanation:

Let the amount of dimes = d.

And the amount of quarters = q.

We can write 2 equations with the given information.

d = q + 7 --- the amount of dimes is 7 more than the amount of quarters

0.1d + 0.25q = 6.3 --- a dime is 0.1 dollars and a quarter is 0.25 dollars

0.1(q + 7) + 0.25q = 6.3 --- we can substitute q + 7 for d because they have the same value and we need to have only 1 variable to solve

0.1q + 0.7 + 0.25q = 6.3 --- distribute multipliers outside the parenthesis

0.35q + 0.7 = 6.3 --- combine like terms

0.35q = 5.6 --- subtract 0.7 from both sides

q = 16 --- divide both sides by 0.35

The cashier has 16 quarters. We can use this to solve for dimes.

d = q + 7

d = 16 + 7

d = 23

The cashier has 23 dimes and 16 quarters.

0.1d + 0.25q = 6.3

0.1(23) + 0.25(16) = 6.3

2.3 + 4 = 6.3

6.3 = 6.3

The answer is correct.

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0