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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