Question

You have been saving nickels, dimes, and quarters in a jar for about a year. You decide to see how much money you've saved up. When you get everything counted it turns out you have 361 total nickels, dimes, and quarters worth a total of $41.45. You think is is odd that you have exactly twice as many dimes as quarters. Find the number of each coin.

Answer 1

No. of Nickels = 127

No. of Dimes = 156

No. of Quarters = 78

Explanation:

First we need to form a system of equations representing the situation. So, first we let:

x = number of nickel coins

y = number of dimes

z = number of quarters

Now, we know that the total coins are 361. Therefore,

x + y + z = 361 ----------- equation (1)

It is also given that there are twice as many dimes as quarters:

y = 2z

y - 2z = 0 ----------------equation (2)

Now, we have a total worth of $41.45. A dime is worth $0.1, nickel is worth $0.05 and a quarter is worth $0.25. Therefore,

0.05x + 0.1y + 0.25z = 41.45 ----------------- equation (3)

Simultaneously solving the three equations, we get:

x = 127, y = 156, z = 78

Hence,

No. of Nickels = 127

No. of Dimes = 156

No. of Quarters = 78