James has 55 dimes in the bag
Step-by-step explanation:
The given is:
- James has in a bag 77 of nickels and dimes
- The total value of coins is $6.60
We need to find how many dimes James has
Assume that the number of nickels is x and the number of
dimes is y in the bag
∵ There are x nickels in the bag
∵ There are y dimes in the bag
∵ There are 77 coins in the bag
∴ x + y = 77 ⇒ (1)
∵ 1 nickel = 5 cents
∴ The value of nickles in the bag = 5x cents
∵ 1 dime = 10 cents
∴ The value of dimes in the bag = 10y cents
∵ The total value of coins is $6.60
∵ 1 dollar = 100 cents
∴ $6.60 = 6.60 × 100 = 660 cents
∴ 5x + 10y = 660 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -10 to eliminate y
∵ -10x - 10y = -770 ⇒ (3)
- Add equations (2) and (3)
∴ -5x = -110
- Divide both sides by -5
∴ x = 22
Substitute the value of x in equation (2) to find y
∵ 22 + y = 77
- Subtract 22 from both sides
∴ y = 55
∴ The number of dimes is 55
James has 55 dimes in the bag
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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