Susie has 2 more dimes than nickels. this amounts to $1.85. how many of each coin does she have? show all of your guesses.

She has 11 nickels and 13 dimes

Step-by-step explanation:

* Lets explain how to solve the problem

- The dime = 10 cents

- The nickel = 5 cents

- Susie has 2 more dimes than nickels

- The amount of money with her is $1.85

- 1 dollar = 100 cents

* Lets solve the problem

- Let the number of dimes is d and the number of nickels is n

∵ Susie has 2 more dimes then nickels

∵ d is the number of dimes and n is the number of nickels

∴ d = n + 2 ⇒ (1)

∵ 1 dime = 10 cents and 1 nickel = 5 cents

∵ The amount of these coins = $1.85

∵ 1 dollar = 100 cents

∴ 10d + 5n = 1.85 × 100

∴ 10d + 5n = 185 ⇒ (2)

- To find the numbers of dimes and nickels substitute equation (1)

  in equation (2)

∴ 10(n + 2) + 5n = 185 ⇒ multiply the bracket by 10

∴ 10n + 20 + 5n = 185 ⇒ add like terms

∴ 15n + 20 = 185

- Subtract 20 from both sides

∴ 15n = 165

- Divide both sides by 15

∴ n = 11

- Substitute the value of n in equation (1)

∴ d = 11 + 2 = 13

∵ n is the number of nickels and d is the number of dimes

∴ She has 11 nickels and 13 dimes