Question

Isabel found 54 coins at the bottom of her backpack. when she looked, she noticed they were only nickels and dimes. Isabel counted the coins and they totaled $4.25. How many nickels and dimes did she have?
Solve algebraically
use systems to solve the word problem

Answer 1

She had 23 nickles and 31 dimes

Step-by-step explanation:

The given is:

• Isabel found 54 coins at the bottom of her backpack
• She noticed they were only nickels and dimes
• Isabel counted the coins and they totaled $4.25

We need to find how many nickels and dimes she had

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

∵ Isabel had 54 coins

∵ The number of nickels is x

∵ The number of dimes is y

∴ x + y = 54 ⇒ (1)

∵ 1 nickle = 5 cents

∵ 1 dime = 10 cents

∵ The coins totaled $4.25

- Change the dollars to cents

∵ 1 dollar = 100 cents

∴ $4.25 = 4.25 × 100 = 425 cents

- Multiply the number of nickles by 5 and the number of dimes

  by 10, add the two products and equate the sum by 425

∴ 5x + 10y = 425 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -540 ⇒ (3)

- Add equations (2) and (3)

∴ -5x = -155

- Divide both sides by -5

∴ x = 23

Substitute the value of x in equation (1) to find y

∵ 23 + y = 54

- Subtract 23 from both sides

∴ y = 31

She had 23 nickles and 31 dimes

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

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