Question

Jalen has $10.35 in quarters and nickels he has a total of 99 coins how many of each coins does he have?

Answer 1

Jalen has 27 quarters and 72 nickels.

Step-by-step explanation:

To solve this problem, let's assign variables to represent the number of quarters and nickels that Jalen has. Let q represent the number of quarters and n represent the number of nickels. Given that Jalen has a total of 99 coins, we can write the equation q + n = 99.

Since a quarter is worth $0.25 and a nickel is worth $0.05, we can also write the equation 0.25q + 0.05n = 10.35.

To solve this system of equations, we can use the method of substitution. Solving the first equation for q, we get q = 99 - n. Substituting this expression for q in the second equation, we get 0.25(99 - n) + 0.05n = 10.35.

Now we can solve for n. Simplifying the equation, we get 24.75 - 0.25n + 0.05n = 10.35. Combining like terms, we have -0.20n = -14.40. Dividing both sides by -0.20, we find that n = 72.

Substituting this value for n in the equation q + n = 99, we can solve for q. Plugging in the values, we get q + 72 = 99. Solving for q, we find that q = 27.

Therefore, Jalen has 27 quarters and 72 nickels.

Answer 2

Answers:

72 nickels and 27 quarters

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Work Shown:

$10.35 = 1035 cents

q = number of quarters

n = number of nickels

n+q = 99 is the total number of coins. This solves to q = -n+99

25q = value of all the quarters in cents

5n = value of all the nickels in cents

5n+25q = 1035 is the total value in cents

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5n+25q = 1035

5n+25( q ) = 1035

5n+25( -n+99 ) = 1035

5n - 25n + 2475 = 1035

-20n + 2475 = 1035

-20n = 1035-2475

-20n = -1440

n = -1440/(-20)

n = 72

Jalen has 72 nickels

q = -n+99

q = -72+99

q = 27

Jalen has 27 quarters

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Check:

n+q = 72+27 = 99

5n+25q = 5*72+25*27 = 1035

This confirms the answers.