Question

Teresa is creating a new cookie recipe. She has discovered the total cups of flour and sugar cannot be more than five and there needs to be at least twice as much flour as sugar. Which of the following graphs represents the possible flour and sugar combination?

Answer 1

Correct answer is option C.

Explanation:

Given:

Number of cups of flour and sugar can not be more than five.

At least twice as much flour as sugar required.

Let
`x` be the number of cups flours needed and

`y` be the number of cups of sugar needed

As per the given conditions:

`x+y\le 5` and

`x \ge 2y`

These are number of cups, so can not be negative.

i.e.
`x\ge0, y\ge0`

First of all, let us convert it to equality and then plot the graph.

`x+y=5\ and\\x=2y`

Let us plot by finding 2 points on each equality.

First equation:

Putting x = 0, y = 5 One point (0,5)

Putting y = 0, x = 5 Another point (5,0)

Putting point (0, 0) in inequality, which is true so shaded region will be towards (0, 0).

Second equation:

Putting x = 0, y = 0 One point (0,0)

Putting x = 1, y = 2 One point (1,2)

Putting point (2, 0) in inequality, which is true so shaded region will be towards (2, 0).

Now let us plot them.

Please refer to the attached image. Shaded region with black strips is the solution.

The attached image is equivalent to option 3rd.