Question

A chef got 7 bags of onions. The red onions came in bags of 8 and the yellow onions came in bags of 3. If the chef got a total of 41 onions, how many bags of each type of onion did he get?

Answer 1

`\#\text{ of 8-onion bags: }4,\\\#\text{ of 3-onion bags: }3`

Explanation:

Let
`a` be the number of bags with 8 onions and let
`b` be the number of bags with 3 onions. We have the following system of equations:

`\begin{cases}a+b=7,\\8a+3b=41\end{cases}`

Subtracting
`b` from both sides of the first equation, we get
`a=7-b`. Substitute this into the second equation:

`8(7-b)+3b=41,\\56-8b+3b=41,\\56-5b=41,\\-5b=-15,\\b=\boxed{3}`

Therefore, the number of 8-onion bags is:

`a=7-b,\\a=7-3,\\a=\boxed{4}`

Thus, the chef got 4 8-onion bags and 3 3-onion bags.