MATH SOLVE

4 months ago

Q:
# You have 64 coins, consisting of pennies, nickels, and quarters. The value ofthe coins is $4.60. You also know that you have three times as many nickels asquarters. Find the quantity of each type of coin.

Accepted Solution

A:

Answer:There are 20 pennies, 33 nickels and 11 quartersStep-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 = 33There are 20 pennies, 33 nickels and 11 quarters