Year 8 Rates and unit comparisons — Hard exercise 17

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In a sports equipment allocation for a regional training camp in Perth, 82 identical basketballs are distributed among 41 teams such that each team receives the same number of basketballs.

What is the exact rate of basketballs per team, expressed as a simplified fraction?

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Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.

With a fixed charge of $4 and $2 per kilometre, cost C = 4 + 2d. At d = 3 km the cost is $10. Assume this tariff applies for the trip.

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Worked solution

The total number of basketballs is 82, and they are to be distributed equally among 41 teams.
To find the rate of basketballs per team, divide the total number of basketballs by the number of teams: 82 ÷ 41.
Set up the fraction: 82 / 41.
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 82 and 41 is 41.
Divide 82 by 41: 82 ÷ 41 = 2.
Divide 41 by 41: 41 ÷ 41 = 1.
The simplified fraction is 2 / 1.
The rate of basketballs per team is therefore 2 basketballs per team.
Verify by multiplication: 41 teams × 2 basketballs per team = 82 basketballs, which matches the total.
The fraction 2/1 is in simplest form and represents the exact rate.
The rate of basketballs per team is exactly 2 basketballs per team.
The solution is complete and matches the required format.

Reference answer: 2 basketballs per team

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