Question

(Answer for 20 points) Penelope is collecting coins to raise money for a charity so far she collected

• twice as many dimes as quarters

• 4 times nickels than dimes, and

• three times as many pennies as quarters

If Penelope has collected 780 coins, how many of each type of coin she collected.

Answer 1

Penelope collected 43 quarters, 86 dimes, 344 nickels, and 129 pennies.

Explanation:

From the problem statement, we know:

d = 2q (Twice as many dimes as quarters)

n = 4d (Four times as many nickels as dimes)

p = 3q (Three times as many pennies as quarters)

• We also know that the total number of coins collected is 780:

q + d + n + p = 780

• We can substitute the first three equations into the fourth equation to get an equation in terms of only one variable:

q + 2q + 4d + 3q = 780

• Simplifying this equation, we get:

10q + 4d = 780

• We can then substitute the first equation above into this equation to get:

10q + 4(2q) = 780

18q = 780

q = 43.33 (rounded to two decimal places)

Since we can't have a fraction of a coin, we need to round down to the nearest whole number. Therefore, Penelope collected 43 quarters.

Using the other equations, we can then find the number of each type of coin:

d = 2q = 2(43) = 86 dimes

n = 4d = 4(86) = 344 nickels

p = 3q = 3(43) = 129 pennies