Question

Brooklyn has a combination of dimes and nickels in her wallet. She has 3 times as many nickels as she does dimes, and the total value of the coins is $4.00. How many does she have of each coin?

Answer 1

She has 16 dimes and 48 nickels in her wallet

Step-by-step explanation:

Brooklyn has a combination of dimes and nickels in her wallet

• She has 3 times as many nickels as she does dimes
• The total value of the coins is $4.00

We need to find how many she has of each coin

Assume that the number of dimes is x and the number of nickels is y

∵ She has x dimes

∵ She has y nickels

∵ She has 3 times as many nickels as many dimes

- That means y is 3 times x

∴ y = 3x ⇒ (1)

∵ 1 dime = 10 cents

∴ The value of dimes = x × 10 = 10x cents

∵ 1 nickel = 5 cents

∴ The value of nickles = y × 5 = 5y cents

∵ The total value of the coins is $4.00

∵ 1 dollar = 100 cent

∴ The total value of the coins = 4 × 100 = 400 cents

- Add 10x and 5y, then equate the sum by 400

∴ 10x + 5y = 400

- Divide all terms by 5 to simplify the equation

∴ 2x + y = 80 ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (2) by equation (1)

∵ 2x + 3x = 80

∴ 5x = 80

- Divide both sides by 5

∴ x = 16

- Substitute x by 16 in equation (1)

∵ y = 3(16)

∴ y = 48

She has 16 dimes and 48 nickels in her wallet

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

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