19
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Set up a system of equations, where the number of tumblers is t and the number of magnets is m.
We are given two pieces of information:
- The total number of items (tumblers and magnets) is 32, so t + m = 32.
- The total cost of items is $135.5, and we know that each tumbler costs $7.5 and each magnet costs $2. Therefore, the cost can be expressed as 7.5t + 2m = 135.5.
Now we have a system of two equations:
- t + m = 32
- 7.5t + 2m = 135.5
We can solve this system using elimination.
Multiply the first equation by 7.5 and then subtract the second one:
- 7.5t + 7.5m - 7.5t - 2m = 32*7.5 - 135.5
- 5.5m = 104.5
- m = 104.5/5.5
- m = 19
So, the manager purchased 19 magnets.
