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You have a total of 25 coins, all nickels and quarters. The total value is

$3.85. Write and solve a system of equations to find the number of
nickels n and the number of quarters q that you have. Can you solve it

1 Answer

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Answer: Yes, I can solve this problem using a system of equations. Let n be the number of nickels and q be the number of quarters. Then we can write two equations:

The total number of coins is 25: n + q = 25.

The total value is $3.85: 0.05n + 0.25q = 3.85

We can solve this system of equations using substitution or elimination. Let's use substitution:

From equation (2), we can solve for n: n = (3.85 - 0.25q)/0.05.

Substitute this expression for n into equation (1): (3.85 - 0.25q)/0.05 + q = 25.

Multiply both sides by 0.05 to clear the denominators: 3.85 - 0.25q + 0.05q = 25 * 0.05.

Simplify the left side: 3.85 = 1.25q.

Divide both sides by 1.25 to solve for q: q = 3.08

Substitute this value for q into equation (1) or the expression for n from step (1) to find n: n = 25 - q = 25 - 3.08 = 21.92

Since n and q represent the number of coins, we round them down to the nearest whole number. So, there are 21 nickels and 3 quarters.

Explanation:

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