Ticket Price Boundary
A museum charges ₱118 for admission. A student has ₱1,000 available. Ticket prices are set in whole-peso amounts.
How many tickets can the student buy?
At ₱118 per ticket
So the greatest number that can be bought is 8 tickets.
Change the ticket price
Try the prices below. Watch what happens to the maximum number of tickets.
Choose a price to change the situation.
Prices you have tested
| Ticket price | Cost of 8 | Maximum tickets |
|---|---|---|
| ₱118 | ₱944 | 8 |
Try another price and compare what happens.
What do you notice?
Does the maximum number of tickets change every time the price changes?
Look more closely
At ₱122, 8 tickets are still possible.
At ₱130, they are not.
Where does the change happen?
Cost of 8 tickets
₱1,000 available
What is the highest ticket price at which 8 tickets can still be bought?
₱125
At ₱125
8 × ₱125 = ₱1,000
8 tickets are still possible.
At ₱126
8 × ₱126 = ₱1,008
8 tickets are no longer possible.
₱125 is the highest whole-peso ticket price for which 8 tickets still fit within the ₱1,000 available.
Why does the answer change between ₱125 and ₱126?
Thinking further
The student still has ₱1,000 available.
If the ticket price keeps increasing, the maximum number of tickets that can be bought with ₱1,000 will eventually drop from 7 to 6.
What is the highest whole-peso ticket price at which the student can still buy 7 tickets with ₱1,000?
₱142
At ₱142 each, 7 tickets cost ₱994.
At ₱143 each, 7 tickets would cost ₱1,001.
The ticket price can change while the maximum number of tickets stays the same. But eventually a boundary is reached: beyond it, the maximum changes.
Looking for where a conclusion changes can reveal more about a situation than calculating one answer alone.