Question

A burger joint offers burgers with 1, 2, and 3 patty options, with and without cheese. What percentage of the orders are 2 patties, no cheese?

• 77% of orders are 1 patty
• 16% of orders are 2 patties
• 42% of orders are 1 patty with cheese
• 2% of orders are 3 patties no cheese
• 54% of all orders have cheese

Answer 1

See below:

Explanation:

We'll start with burger patties on top. Burgers with cheese will be in `color(green)"green"` and with no cheese will be in `color(red)("red")`

`color(white)(0)1color(white)(00000000000000)2color(white)(0000000000000)3color(white)(00000)"Burger patties"`

`77%color(white)(0000000000)16%color(white)(00000000000)7%`

`/color(white)(000)"\"color(white)(0000000000)"/"color(white)(00)"\"color(white)(0000000000)"/"color(white)(000)"\"`

`color(white)(0)|color(white)(000000)"|"color(white)(00000000)"|"color(white)(00000)"|"color(white)(00000000)"|"color(white)(00000)"|"color(white)(00000)`

`color(green)("42%")color(white)(0000)color(red)("35%")color(white)(00000)color(green)("7%")color(white)(000)color(red)("9%")color(white)(000000)color(green)("5%")color(white)(000)color(red)("2%")color(white)(0)"Percentage of orders in total"`

Ok - how to do this:

We know there are 3 types of burger options: 1 patty, 2 patties, 3 patties and these will add to 100%:

`77%+16%+"3 patties"=100%`

`"3 patties"=7%`

We know that `42%` of the orders are 1 patty with cheese. This means that the remaining percentage of single patty burgers are no cheese:

`42%+"1 patty no cheese"=77%`

`"1 patty no cheese"=35%`

We know that `2%` of all orders are the 3 patties no cheese. Which means the remaining amount has cheese:

`2%+"3 patties with cheese"=7%`

`"3 patties with cheese"=5%`

We know that 54% of all orders have cheese. We know the total orders for 1 and 3 patties, so we can solve for 2 patties:

`42%+"2 patties with cheese"+5%=54%`

`"2 patties with cheese"=7%`

And lastly we can figure out the number of 2 patties no cheese:

`7%+"2 patties no cheese"=16%`

`"2 patties no cheese"=9%`