How to Solve Coin Problems Part 2

I have already introduced how to solve coin problems, so in this post, we solve more problems about it. Coin problems involve problems consisting coins, bills, and of course, any object of value. We have already solved 2 problems in the previous post, so we continue with the third problem.

Problem 3

A box contains 32 bills consisting of Php20 and Php50. The total amount of money in the box is 1000 pesos. How many bills of each kind are there?

Note: For my readers from other countries, Php means Philippine pesos.

Solution

This problem is similar to problem 2, so we will not be solving it in details.

Let be the number of 50-peso bills. Since there are 32 bills, then the number of 20-peso bills is Now, if we multiply the number of 50-peso bills by 50 pesos and multiply the number of 20-peso bills by 20 pesos, we have

and

respectively.

If we add them, the total is 1000 pesos. That is,

.

Simplifying and solving for , we have

Subtracting both sides by 640, we have

.

Dividing both sides by 30, we have

.

Therefore, the number of 50-peso bills is 12. Now, since there are 32 bills, the number of 20-peso bills is 32-12 = 20.

Check

12(Php50) + 20(Php20) = Php600 + Php400 = Php1000

Problem 4

In a charity musical show, there are the same number of tickets sold worth $20, $50, and $100. The total cost of the tickets is $5100.

Solution

Let be the number of tickets sold.  Since there are the same number of tickets, if we multiply the number of ticket to each of the price, we have

, and

which are the total cost of each kind. If we add them all together, then, it is the total cost of all the tickets which is $5100. That is,

.

Simplifying, we have

Dividing both sides by , we have

.

This means that there are 30 tickets of each price that were sold.

Check

$20(30) + $50(30) + $100(30) = $600 + $1500 + $3000 = $5100.

In the next part of this post, we will solve two more problems to end this series.