If you have three quarters four dimes and four cents you have 1 19 but you cannot make exact change for a dollar

If you have three quarters, four dimes and four cents, you have $1.19. But you cannot make exact change for a dollar.

Have you ever wondered if you can make exact change for a dollar with a combination of coins? Well, if you have three quarters, four dimes, and four cents in your possession, you might think that you have $1.19, which should be enough to exchange for a dollar bill. Surprisingly, this is not the case. Despite having a total value equivalent to more than a dollar, you cannot make exact change for a dollar with these specific coins. Let’s delve into why this is so.

One might assume that since three quarters amount to $0.75, adding four dimes (valued at $0.10 each) would result in $0.75 + $0.40, equaling $1.15. Finally, adding four pennies (with a value of $0.01 each) would give us an excess of $0.04, enough to round up to a dollar. But unfortunately, the math doesn’t add up.

To understand why we cannot make exact change for a dollar with these coins, we need to focus on the denominations themselves. Quarters, dimes, and pennies are the common denominations in circulation, but the absence of nickels poses a challenge in this particular scenario.

Nickels, worth $0.05 each, would have bridged the gap between $1.15 and $1.19, allowing us to make exact change. However, without nickels, we are left with an extra $0.04, which does not correspond to any available coin. This means that despite having a value of $1.19, it is impossible to exchange these coins for a single dollar bill.

But why is it that nickels can act as a bridge between the quarters and dimes? The reason lies in their divisibility. A nickel can be split into five equal parts, worth $0.01 each. Therefore, by using nickels, one can precisely fill in the gap between $1.15 and $1.19. However, as we lack nickels in this scenario, reaching the exact dollar amount becomes impossible.

In conclusion, despite having a total value of $1.19, the combination of three quarters, four dimes, and four cents falls short of being able to make exact change for a dollar. This peculiarity arises from the absence of nickels, which are necessary to bridge the gap between $1.15 and $1.19. So, next time you find yourself with these particular coins, keep in mind that even though they amount to more than a dollar, they cannot be exchanged for that precise amount.

(Source: Wyzant)