Solve this probiem using a system of equations; Colin has a jar of quarters and nickels, The jar has 15 coins
atrogether, The total value of the coins is . How many of each coin does Colin have?

Question

Solve this probiem using a system of equations; Colin has a jar of quarters and nickels, The jar has 15 coins
atrogether, The total value of the coins is

. How many of each coin does Colin have?

UpStudy AI · Accepted Answer

Let $$ q $$ be the number of quarters and $$ n $$ be the number of nickels.

1. Write the system of equations:
   - Total coins: 
     $$
     q + n = 15
     $$
   - Total value (in dollars): 
     $$
     0.25q + 0.05n = 2.75
     $$

2. Multiply the value equation by 100 to eliminate decimals:
   $$
   25q + 5n = 275
   $$

3. Divide the equation by 5:
   $$
   5q + n = 55
   $$

4. Subtract the equation $$ q + n = 15 $$ from $$ 5q + n = 55 $$:
   $$
   (5q + n) - (q + n) = 55 - 15
   $$
   $$
   4q = 40
   $$

5. Solve for $$ q $$:
   $$
   q = \frac{40}{4} = 10
   $$

6. Substitute $$ q = 10 $$ into the total coins equation:
   $$
   10 + n = 15
   $$
   $$
   n = 15 - 10 = 5
   $$

Colin has $$10$$ quarters and $$5$$ nickels.
Colin has 10 quarters and 5 nickels.

Solve this probiem using a system of equations; Colin has a jar of quarters and nickels, The jar has 15 coins
atrogether, The total value of the coins is . How many of each coin does Colin have?

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Solve this probiem using a system of equations; Colin has a jar of quarters and nickels, The jar has 15 coins atrogether, The total value of the coins is . How many of each coin does Colin have?

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Solve this probiem using a system of equations; Colin has a jar of quarters and nickels, The jar has 15 coins
atrogether, The total value of the coins is . How many of each coin does Colin have?