P5 Guess and Check: Choose Practice That Reveals the Method

Choose a task that makes the decisions visible

Useful guess-and-check practice asks a child to explain how each trial changes the total. For today's ticket challenge, begin with all child tickets and notice what happens when one is replaced by an adult ticket. A guess becomes useful when it helps choose the next one.

For families using Zairoo.Ai, keep the first attempt and the corrections visible on paper. This P5 challenge needs multiplication, division and money calculations, plus an understanding that the number of tickets stays fixed. It does not require simultaneous equations.

The challenge

A family group buys 24 tickets. Adult tickets cost S$8 each and child tickets cost S$5 each. The group pays S$147 altogether. How many adult and child tickets did it buy?

There are two conditions to preserve: the count is 24 and the cost is S$147. A pair of counts that adds to 24 can still give the wrong price. A price calculation that reaches S$147 is not enough if the ticket count changes along the way.

The P5 methods and model-drawing guide includes guess-and-check and supposition approaches. Use the word-problem methods guide to help your child connect a method to the information in the story.

Give the first guess a purpose

Start with 6 adults and 18 children, keeping the total ticket count fixed.

Adult cost: 6 x 8 = S$48

Child cost: 18 x 5 = S$90

Combined cost: 48 + 90 = S$138

Amount still needed: 147 - 138 = S$9

Extra cost per replacement: 8 - 5 = S$3

Replacements needed: 9 / 3 = 3

New adult count: 6 + 3 = 9

New child count: 18 - 3 = 15

The same replacement idea also works from the all-child starting point shown below.

Visual model and step by step solution

Step 1 Suppose all tickets are child tickets

24 x 5 = S$120

Step 2 Find the cost increase needed

147 - 120 = S$27

Step 3 Replace one child ticket with one adult ticket

8 - 5 = S$3 extra per replacement.

27 / 3 = 9 adult tickets

Step 4 Find the number of child tickets

24 - 9 = 15 child tickets

Answer: 9 adult tickets and 15 child tickets.

Check against the question

Count: 9 + 15 = 24

Adults: 9 x 8 = S$72

Children: 15 x 5 = S$75

Total: 72 + 75 = S$147

The misconception to notice

A child may divide the S$27 excess by S$8, using the full adult price. But the S$120 starting total already paid S$5 for each ticket. Only the additional S$3 matters when replacing a child ticket.

Another child may add adults without removing children. Point to the fixed count of 24 and ask which existing ticket changes. The replacement must alter the type, not create an extra ticket.

Parent prompts

Ask, "Which condition does your first guess already satisfy?" Then, "If one ticket changes type, what changes and what stays the same?" Finally, "How can you choose the next guess using the amount you are short?"

These questions reveal the method without announcing the correct counts. Ask your child to explain their adjustment before calculating the new total.

Fresh retry with a worked solution

There are 30 adult and child tickets altogether. Adults cost S$9 each; children cost S$6 each. The total is S$216, with no other fees. Find both counts.

Pause for an independent attempt before reading the model and solution.

Step 1 Suppose all tickets are child tickets

30 x 6 = S$180

Step 2 Find the cost increase needed

216 - 180 = S$36

Step 3 Replace one child ticket with one adult ticket

9 - 6 = S$3 extra per replacement.

36 / 3 = 12 adult tickets

Step 4 Find the number of child tickets

30 - 12 = 18 child tickets

Answer: 12 adult tickets and 18 child tickets.

Check against the question

Count: 12 + 18 = 30

Adults: 12 x 9 = S$108

Children: 18 x 6 = S$108

Total: 108 + 108 = S$216

A multi step extension

A group buys 30 tickets. Adult tickets cost S$9 each and child tickets S$6 each. The group pays S$237, including one S$12 booking fee for the entire order. Find the adult and child ticket counts. There are no other charges or ticket types.

Step 1 Remove the one off booking fee

237 - 12 = S$225 for tickets only.

Step 2 Suppose all tickets are child tickets

30 x 6 = S$180

Step 3 Find the cost increase needed

225 - 180 = S$45

Step 4 Replace one child ticket with one adult ticket

9 - 6 = S$3 extra per replacement.

45 / 3 = 15 adult tickets

Step 5 Find the number of child tickets

30 - 15 = 15 child tickets

Answer: 15 adult tickets and 15 child tickets.

Check against the question

Count: 15 + 15 = 30

Adults: 15 x 9 = S$135

Children: 15 x 6 = S$90

Total: 135 + 90 + 12 = S$237

Extension retry with a worked solution

There are 24 tickets. Adults cost S$10 and children S$6. The total S$200 includes one S$8 booking fee. Find both ticket counts.

Try this independently before checking the solution.

Step 1 Remove the one off booking fee

200 - 8 = S$192 for tickets only.

Step 2 Suppose all tickets are child tickets

24 x 6 = S$144

Step 3 Find the cost increase needed

192 - 144 = S$48

Step 4 Replace one child ticket with one adult ticket

10 - 6 = S$4 extra per replacement.

48 / 4 = 12 adult tickets

Step 5 Find the number of child tickets

24 - 12 = 12 child tickets

Answer: 12 adult tickets and 12 child tickets.

Check against the question

Count: 12 + 12 = 24

Adults: 12 x 10 = S$120

Children: 12 x 6 = S$72

Total: 120 + 72 + 8 = S$200

FAQs

Is an initial wrong guess wasted? No, if your child uses its difference from the target to adjust systematically.

Must everyone use the all-child start? No. Any correct organised approach should preserve the count and explain the cost changes.

Source note: These ticket challenges are original editorial practice, not official exam questions.

For the next session with Zairoo.Ai, choose one task and ask your child to explain why the next guess is better than the first.