Question

svlc algebra 1a - standard (15260)
solving mixture problems
ari has a total of 22 coins consisting of pennies and nickels. the total value of the coins is $0.54. how many pennies does
the have?
let p represent the number of pennies. complete the table to organize this information.
0.05 0.05(22 - p) 0.01p p 22 - p 0.01 0.54 22
drag each tile to the correct cell in the table.

	number	value	total value
nickels
total

Explanation:

Step1: Define Variables for Pennies

Let \( p \) be the number of pennies. The value of one penny is \( \$0.01 \), so the value of \( p \) pennies is \( 0.01p \). The number of pennies is \( p \), the value per penny is \( 0.01 \), and the total value for pennies is \( 0.01p \).

Step2: Define Variables for Nickels

The total number of coins is 22, so the number of nickels is \( 22 - p \). The value of one nickel is \( \$0.05 \), so the total value of nickels is \( 0.05(22 - p) \). The number of nickels is \( 22 - p \), the value per nickel is \( 0.05 \), and the total value for nickels is \( 0.05(22 - p) \).

Step3: Total Row

The total number of coins is 22, the total value per coin isn't a separate value here, and the total value of all coins is \( \$0.54 \).

Now, filling the table:

• Pennies Row:
• Number: \( p \)
• Value: \( 0.01 \)
• Total Value: \( 0.01p \)

• Nickels Row:
• Number: \( 22 - p \)
• Value: \( 0.05 \)
• Total Value: \( 0.05(22 - p) \)

• Total Row:
• Number: \( 22 \)
• Value: (not applicable in the same way, but the total value is \( 0.54 \))
• Total Value: \( 0.54 \)

To solve for \( p \) (number of pennies), we can set up the equation:

\( 0.01p + 0.05(22 - p) = 0.54 \)

Step4: Solve the Equation

Expand the equation:

\( 0.01p + 1.1 - 0.05p = 0.54 \)

Combine like terms:

\( -0.04p + 1.1 = 0.54 \)

Subtract 1.1 from both sides:

\( -0.04p = 0.54 - 1.1 \)

\( -0.04p = -0.56 \)

Divide both sides by -0.04:

\( p = \frac{-0.56}{-0.04} = 14 \)

Answer:

The number of pennies \( p \) is 14. And the table is filled as:

	Number	Value	Total Value
Nickels	\( 22 - p \)	0.05	\( 0.05(22 - p) \)
Total	22	-	0.54

And the number of pennies is 14.