"Jack has a collection of nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have?" I got the answer of 39 quarters and 11 nickels by trial and error. Can someone tell me the correct way to set the problem up? Thank you.

bgrtyuio;

To solve this problem algebraically, you can set up a system of linear equations. Let's assign variables to the unknown quantities: let 'x' represent the number of nickels and 'y' represent the number of quarters.

First, we need to establish two equations based on the given information. The first equation relates to the quantity of coins: x + y = 50. This equation states that the total number of nickels and quarters is 50.

The second equation relates to the value of the coins: 0.05x + 0.25y = 10.30. This equation represents the total value of the nickels and quarters, where 0.05 represents the value of each nickel, and 0.25 represents the value of each quarter.

Now, you have a system of equations:

Equation 1: x + y = 50
Equation 2: 0.05x + 0.25y = 10.30

To solve the system, we can either use substitution or elimination method. Let's solve it using the elimination method.

Multiply both sides of Equation 1 by 0.05 to make the coefficients of x in both equations equal:

0.05(x + y) = 0.05(50)
0.05x + 0.05y = 2.50

Now, subtract this equation from Equation 2:

0.05x + 0.25y - (0.05x + 0.05y) = 10.30 - 2.50
0.25y - 0.05y = 7.80

Combine the like terms:

0.20y = 7.80

Divide both sides by 0.20:

y = 7.80 / 0.20
y = 39

Now that we have the number of quarters (y = 39), we can substitute this value into Equation 1 to find the number of nickels (x):

x + 39 = 50
x = 50 - 39
x = 11

So, the correct answer is that Jack has 11 nickels and 39 quarters in his collection.

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12

bababooy i need help with this uhhh daddy chill ok no yes no

0010101101010100010101110101001010110110010010101001

sure. If there are n nickels, then there must be 50-n quarters, since there are 50 coins in all.

Now, add up the values of the coins:

5n + 25(50-n) = 1030
n = 11

ur mommmmm