A manager bought lunch for his coworkers. Each person picked either a salad or a burger. The salads cost $5 each and the burgers cost $2 each. If the manager spent $15 and bought lunch for 6 people, how many of each item did he buy?
Question
A manager bought lunch for his coworkers. Each person picked either a salad or a burger. The salads cost 2 each. If the manager spent $15 and bought lunch for 6 people, how many of each item did he buy?
Solution
Let's denote the number of salads as S and the number of burgers as B.
From the problem, we know two things:
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The total number of items (salads and burgers) is 6. So, we can write this as an equation: S + B = 6.
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The total cost of the items is 5 and each burger costs $2, we can write this as another equation: 5S + 2B = 15.
Now we have a system of two equations, and we can solve it step by step:
First, let's multiply the first equation by 2: 2S + 2B = 12.
Then, subtract this new equation from the second one: 5S + 2B - (2S + 2B) = 15 - 12. This simplifies to 3S = 3.
Finally, divide both sides of this equation by 3 to solve for S: S = 1.
Substitute S = 1 into the first equation: 1 + B = 6. Solve for B: B = 5.
So, the manager bought 1 salad and 5 burgers.
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