Answer:
There are 20 pennies, 33 nickels and 11 quarters
Step-by-step explanation:
- You have 64 coins, consisting of pennies, nickels, and quarters
- The value of the coins is $4.60
- Assume that there are p pennies, n nickles, and q quarters
∴ p + n + q = 64 ⇒ (1)
- Lets find the value of each types of coins
∵ 1 penny = 1 cent ⇒ p = p cents
∵ 1 nickel = 5 cents ⇒ n = 5n cents
∵ 1 quarter = 25 cents ⇒ q = 25q cents
∵ 1 dollar = 100 cents ⇒ $4.60 = 4.60 × 100 = 460 cents
∴ p + 5n + 25q = 460 ⇒ (2)
- You also know that you have three times as many nickels as quarters
∴ n = 3q ⇒ (3) ⇒ the number of nickles by quarters
∵ 5n = 5(3q)
∴ 5n = 15q ⇒ (4) ⇒ the values of nickles by quarters
- Substitute (3) in equation (1) and (4) in equation (2)
∴ p + 3q + q = 64
∴ p + 4q = 64 ⇒ (5)
∴ p + 15q + 25q = 460
∴ p + 40q = 460 ⇒ (6)
- Subtract equation (5) from equation(6) to eliminate p
∴ 36q = 396
- Divide both sides by 36
∴ q = 11
- Substitute the value of q in equation (5)
∴ p + 4(11) = 64
∴ p + 44 = 64
- Subtract 44 from both sides
∴ p = 20
- Substitute the value of q in (3)
∴ n = 3(11) = 33
∴ n = 33
There are 20 pennies, 33 nickels and 11 quarters
Answer:
There are 20 pennies, 33 nickels and 11 quarts.
Step-by-step explanation:
We are given the following information in the question:
1 penny = 1 cent
1 nickel = 5 pennies = 5 cent
1 quarter = 25 pennies = 25 cents
Let x be the number of pennies, y be the number of nickels and z be the number of quarts.
Total number of coins = 64
Amount of money = $4.60 = 460 cents
The, we have the following equations:
[tex]x +y +z =64\\x + 5y + 25z = 460[/tex]
Also, we have three times as many nickels as quarters.
[tex]y = 3z[/tex]
Putting this value in the above equation:
[tex]x + 4z =64\\x + 40z = 460[/tex]
Solving the two equation, we have
x = 20, z = 11
[tex]y = 3z = 33[/tex]
Hence, there are 20 pennies, 33 nickels and 11 quarts.
