Ms Lukezich needs to order sports equipment for the gym. There will be a maximum of \(40\) students using the equipment at any time. She needs the following equipment:
one soccer ball for each pair of students
one parachute for each group of \(10\) students
three tennis balls for each group of \(4\) students
One soccer ball costs \(\$4.\) One parachute costs \(\$25.\) One tennis ball costs \(\$2.\)
How much will it cost to buy all of the required equipment?
One way to solve this is to figure out the maximum number of groups that could be using each piece of equipment. We will do this by assuming we have \(40\) students, since that is the maximum number of students using the equipment at any time.
Since she needs \(1\) soccer ball for every \(2\) students, Ms Lukezich needs \(40 \div 2 = 20\) soccer balls.
The soccer balls will cost a total of \(20 \times \$4 = \$80.\)
Since she needs \(1\) parachute for every \(10\) students, Ms Lukezich needs \(40 \div 10 = 4\) parachutes.
The parachutes will cost a total of \(4 \times \$25 = \$100.\)
Since she needs \(3\) tennis balls for every \(4\) students, Ms Lukezich needs \(40 \div 4 = 10\) sets of \(3\) tennis balls. Thus, she needs \(10 \times 3 = 30\) tennis balls altogether.
The tennis balls will cost a total of \(30 \times \$2 = \$60.\)
Therefore, the total cost for the sports equipment is \(\$80 + \$100 + \$60 = \$240.\)
Alternatively, we could make a table for each piece of equipment to determine how much each will cost. First, we make a table for the soccer balls.
| Number of Soccer Balls | Number of Students | Total Cost, in $ |
|---|---|---|
| \(1\) | \(2\) | \(4\) |
| \(2\) | \(4\) | \(8\) |
| \(3\) | \(6\) | \(12\) |
| \(4\) | \(8\) | \(16\) |
| \(5\) | \(10\) | \(20\) |
We could continue writing out rows in the table until we determine that \(20\) balls meets the needs of \(40\) students, for a cost of \(\$80\). Or we might notice at this point that since \(40 = 4 \times 10\), then the cost of soccer balls for \(40\) students is equal to \(4\) times the cost of soccer balls for \(10\) students. So the cost for the soccer balls is \(4\times \$20 = \$80\).
Next, we make a table for the parachutes.
| Number of Parachutes | Number of Students | Total Cost, in $ |
|---|---|---|
| \(1\) | \(10\) | \(25\) |
| \(2\) | \(20\) | \(50\) |
| \(3\) | \(30\) | \(75\) |
| \(4\) | \(40\) | \(100\) |
So the cost for the parachutes is \(\$100\).
Finally, we make a table for the tennis balls. Note that one set of \(3\) tennis balls costs \(3 \times \$2 = \$6\).
| Number of Sets of 3 Tennis Balls | Number of Students | Total Cost, in $ |
|---|---|---|
| \(1\) | \(4\) | \(6\) |
| \(2\) | \(8\) | \(12\) |
| \(3\) | \(12\) | \(18\) |
| \(4\) | \(16\) | \(24\) |
| \(5\) | \(20\) | \(30\) |
We could continue writing out rows in the table until we determine that \(10\) sets of tennis balls meets the needs of \(40\) students for a cost of \(\$60\). Or, we might notice at this point that since \(40 = 2 \times 20\), then the cost of the tennis balls for \(40\) students is equal to \(2\) times the cost of tennis balls for \(20\) students. So the cost for the tennis balls is \(2\times \$30= \$60\).
Once again, we get a total cost of \(\$80 + \$100 + \$60 = \$240\) for the sports equipment.