# Introduction to Coin Problems

By | April 1, 2014

Coin problems is one of the word problem types that may also appear in the next Civil Service Examination. Coin problems may refer problems regarding actual coins or even problems involving bills. Although the Civil Service Examination is solely for Filipinos, nobody will prevent the creators of the exams using American terms such as pennies, nickels, and dimes.  In case you do not know, or you have forgotten, a penny is equivalent to 1 cent, a nickel is equivalent to 5 cents, and a dime is equivalent to 10 cents.

Let us try to solve two problems as a teaser to this series.

Problem 1

Bingbong has 18 coins in his pocket. Three of them are nickels and five of them are pennies. If the remaining coins are dimes, how much money does Bingbong in his pocket?

Solution

There are 3 nickels and a nickel is 5 cents, so the three nickels are worth 15 cents.

There are 5 pennies and each penny is 1 cent, so 5 pennies are worth 5 cents.

There are 10 coins left, each of which is a dime or 10 cents. Therefore, there is 1.00 peso.

So, Bingbong has 0.15 + 0.05 + 1.00 = P1.20.

Therefore, Bingbong has one peso and 20 cents.

Problem 2

Jamie has 18 bills in her wallet worth 20 pesos and 50 pesos. If the bills totaled to 660 pesos, how many 20-peso and 50-peso are there?

Solution

There are 18 bills and for example, there are five 20-peso bills, then we will be left with $18-5 = 13$ fifty-peso bills. This means that if there are $x$ 20-peso bills, then there are $(18 - x)$ 50-peso bills.

Now, if we multiply the amount and the number of coins, we have $20x$ for the 20-peso coin and $50(18-x)$ for the 50-peso coin. If we add these total amounts, we have 660 pesos. Therefore, we can form the equation

$20x + 50(18-x) = 660$

By distributive property, we have

$20x + 900 - 50x = 660$

Simplifying, we have

$-30x + 550 = 660$

Subtracting 550 from both sides, we have

$-30x = -240$

Dividing both sides by $-30$, we have $x = 8$.

Therefore there are $8$ twenty-peso coins and $10$ fifty-peso bills.

Check

The total amount for the 20-peso bill is 8(20) = 160.

The total amount for the 50-peso bill is 10(50) = 500.

In the next post in this series, we will be discussing more coin problems.