There are 56 nickels in the jar
Step-by-step explanation:
The given is:
We need to find how many nickles in the jar
Assume that the number of nickles is x and the number of quarters is y
∵ There are x nickles in the jar
∵ There are y quarters in the jar
∵ There are 108 coins in the jar
- Equate the sum of x and y by 108
∴ x + y = 108 ⇒ (1)
∵ 1 nickle = 5 cents
∵ 1 quarter = 25 cents
- Multiply x by 5 and y by 25 to find the value of the coins in the jar
∴ The value of the coins in the jar = 5x + 25y cents
∵ The value of the coins is $15.80
- Change dollars to cents
∵ 1 dollar = 100 cents
∴ $15.80 = 15.80 × 100 = 1580 cents
- Equate the value of the coins by 1580
∴ 5x + 25y = 1580
- Simplify the equation by dividing each term by 5
∴ x + 5y = 316 ⇒ (2)
Now we have a system of equation to solve it
Subtract equation (1) from equation (2) to eliminate x
∵ (x - x) + (5y - y) = 316 - 108
∴ 4y = 208
- Divide both sides by 4
∴ y = 52
Substitute the value of y in equation (1) to find x
∵ x + 52 = 108
- Subtract 52 from both sides
∴ x = 56
∴ The number of nickels is 56
There are 56 nickels in the jar
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You can learn more about the system of equations in brainly.com/question/6075514
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