Question

Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many quarters does he have

Answer 1

Answer:

He has 11 quarters

Step-by-step explanation:

* Lets study the information in the problem to solve it

- The value of dimes and quarters is $6.35

- There are dimes and quarters

- The dime = 10 cents

- The quarter = 25 cents

* We must change the money from dollars to cents

∵ $1 = 100 cents

∴ $6.35 = 6.35 × 100 = 635 cents

- The number of dimes = 3 + 3 × number of quarters

* Let number of dimes is D and number of quarter is Q

∴ D = 3 + 3Q

∴ 10D + 25Q = 635

* Substitute the value of D from first equation in the second equation

∴ 10(3 + 3Q) + 25Q = 635 ⇒ open the bracket

∴ 10(3) + 10(3Q) + 25Q = 635

∴ 30 + 30Q + 25Q = 635 ⇒ collect like terms

∴ 30 + 55Q = 635 ⇒ subtract 30 from both sides

∴ 55Q = 605 ⇒ divide both sides by 55

∴ Q = 11

* He has 11 quarters