Answer:
There are 25 nickels, 28 dimes and 3 quarters
Step-by-step explanation:
- Ariel has a collection of coins
- Her collection is worth $4.80
- She has nickels, dimes, and quarters
- The number of nickels that she has is 6 less than the total number of
dimes and quarters
- The number of dimes is equal to the sum of the number of nickels
and quarters
- Assume that the number of nickels is x , the number of dimes is y and
the number of quarters is z
∵ 1 nickel = 5 cents
∵ 1 dime = 10 cents
∵ 1 quarter = 25 cents
∵ 1 dollar = 100 cent
∵ Her collection worth $4.80
∵ 4.80 dollars = 4.80 × 100 = 480 cents
∴ 5x + 10y + 25z = 480 ⇒ (1)
∵ The number of nickels is 6 less than the total number of dimes
and quarters
∴ x = y + z - 6 ⇒ (2)
∵ The number of dimes is equal to the sum of the number of nickels
and quarters
∴ y = x + z
- subtract z from both sides
∴ x = y - z ⇒ (3)
- <em>Equate equation (2) and (3)</em>
∴ y - z = y + z - 6
- Subtract y from both sides
∴ - z = z - 6
- Add 6 to both sides
∴ 6 - z = z
- Add z to both sides
∴ 6 = 2z
- Divide both sides by 2
∴ z = 3
- <em>Substitute the value of z in equation (3)</em>
∴ x = y - 3
- <em>Substitute x and z in equation (1)</em>
∴ 5(y - 3) + 10y + 25(3) = 480
∴ 5y - 15 + 10y + 75 = 480
∴ 15y + 60 = 480
- subtract 60 from both sides
∴ 15y = 420
- Divide both sides by 15
∴ y = 28
- <em>Substitute value of y in equation (3)</em>
∴ x = 28 - 3
∴ x = 25
* <em>There are 25 nickels, 28 dimes and 3 quarters</em>
