A woman has 21 total coins in her pocket, all of which are either dimes or quarters. If the total value of her change is $3.90, how many dimes and how many quarters does she have? Write the number of dimes, then the number of quarters separated by a comma.
Accepted Solution
A:
Answer with Step-by-step explanation:Let there be d dimes and q quartersA woman has 21 total coins in her pocket.⇒ d+q=21 ------(1)1 dime=$ 0.11 quarter=$ 0.25The total value of her change is $3.90⇒ 0.1d+0.25q=3.90Multiplying both sides by 100,we get10d+25q=390 --------(2)(2)-10×(1)10d+25q-10d-10q=390-21015q=180Dividing both sides by 15, we getq=12Putting value of q in (1),we getd=9Hence, Number of dimes=9and number of quarters=12 Write the number of dimes, then the number of quarters separated by a comma.9,12