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A chef got 10 bags of onions. The red onions came in bags of 5 and the yellow onions came in bags of 8. If the chef got a total of 65 onions, how many bags of each type of onion did he get?

Question

A chef got 10 bags of onions. The red onions came in bags of 5 and the yellow onions came in bags of 8. If the chef got a total of 65 onions, how many bags of each type of onion did he get?

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Solution

Let's denote the number of bags of red onions as R and the number of bags of yellow onions as Y.

From the problem, we know two things:

  1. R + Y = 10 (The total number of bags is 10)
  2. 5R + 8Y = 65 (The total number of onions is 65)

We can solve this system of equations step by step:

Step 1: Solve the first equation for R: R = 10 - Y

Step 2: Substitute R in the second equation: 5(10 - Y) + 8Y = 65

Step 3: Simplify the equation: 50 - 5Y + 8Y = 65

Step 4: Combine like terms: 50 + 3Y = 65

Step 5: Subtract 50 from both sides: 3Y = 15

Step 6: Divide both sides by 3: Y = 5

Step 7: Substitute Y = 5 into the first equation: R = 10 - 5 = 5

So, the chef got 5 bags of red onions and 5 bags of yellow onions.

This problem has been solved

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