Emily wants to buy turquoise stones on her trip to New Mexico to give to at least 4 of her friends. The gift shop sells two types of turquoise stones for either $4 or $6 per stone.

Question

Emily has NO MORE than $30 to spend.

(a) write a system of inequalities describing the situation. Be sure to define your variables.

(b) list three possible solutions.

Answer 1

4F + 6S < 30, divide by 2

2F + 3S < 15

F+S > 4

2F + 2S > 8

8< 2F+2S < 2F + 3S < 15

Graph 2 lines, using the above equations, ignoring the inequalities, and you get 2 downward sloping lines.

One goes from (0,4) to (4,0) the other lies above that going from (0,7.5) to (5,0)

the area between those two lines to the right of the y axis and above the x axis that includes the solutions to the constraints

Since the solution involves only integers. it's only the integers within that area that are feasible

5F, 0S

4F, 0 or 1S

3F, 1, 2 or 3S

2F, 2 or 3S

1F, 3,4,5 or 6S

0F, 4,5, or 6 S

15 possibilities within the budget and at least 4

Answer 2

Hi Taylor,

Here we will set up the system of inequalities in the same way we would set up a system of equations, only substituting the = for a < , <= , > , >= where applicable.

a.

Let x = number of stone type 1

Let y = number of stone type 2

We know that Emily will buy at least 4 stones, so x + y will be at least 4. We know that stone 1 costs $4 and stone 2 costs $6, and that she will not spend more than $30. So

x + y >=4

4x+6y<30

b.

Here you would just find values of x and y that meet the above criteria.

3 of type 1, 1 of type 2

If Emily buys 3 of type 1 and 1 of type 2, she will be buying at least 4 stones and will not be spending more than $30.

x + y = 3 + 1 = 4

4 is greater than or equal to 4

4x + 6y = 4(3) + 6(1) = 12 + 6 = $18

$18 is less than $30

See if you can find two more possible solutions yourself!

Answer 3

So this is an alternative way I was working on before someone else answered the question. :p The previous tutor's answer works just as well possibly even quicker! This was just the easiest way for me to think of it....