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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