🎈 Balloons all the way round the room

A closer look at one question · SMC 2024, Question 24 (bank id B9)

Jamie decorated a square classroom of side 6 m 40 cm with a string of balloons that runs once around it. Every 80 cm of string carries 4 small balloons (with big balloons between them). How many small balloons did she use on all 4 sides?

1 Turn the whole room into one length of string

The room is a square of side 6 m 40 cm = 640 cm. Going once round all 4 sides, the string is 4 × 640 = 2560 cm long.

String

2560 cm, once around the square

2 Count how many 80 cm repeats fit

The pattern repeats every 80 cm, so it repeats 2560 ÷ 80 = 32 times.

80cm

⋯

80cm

32 repeats of 80 cm laid end to end around the room

3 Each repeat carries 4 SMALL balloons

1 repeat

4 small balloons (+ big ones between)

32 repeats × 4 small balloons = 128.

128 small balloons

The trap: working out the balloons for one side and forgetting to multiply by 4, or counting the BIG balloons too. The question asks only for the small ones.