# How to graph system of equations.

I have solved every question except show the information on a graph and find the number of each type of tent that must be hired; I have put my problem in quotations, down below in the midst of the entire question. I will show my work, for the other questions they ask.

For a camp of 144 children, two types of tent are available for hire. The large tent sleeps 8 and cost £48 per week, and, the small tent sleeps 3 and cost £12 per week.

The total number of tents must not exceed 36.

Using L for the number of large tents and S for the number of small tents write down inequalities to describe the constraints of: 1 the number of children, 2 the number of tents.

Write down an expression to show the cost of hiring these tents.

If the cost of hiring is to be kept as small as possible, "show the information on a graph and find the number of each type of tent that must be hired."

What will be the total cost of hiring for one week?

You will first, need to set-up a system of equations, for the problem, the number of children, and, the number of tents. Using L, for large and, using S, for small; we come up with:

$$8L + 3S\geq 144$$ $$L + S\le 36$$

The equation for total cost in one week is: $£(48L + 12S)$, which equals $708$.

Turning this into a graph has me stumped!

You can easily turn this into a graph using X and Y intercepts.

Let's make L the x axis and S the y axis For the first equation, the intercepts would be $(18,0)$ and $(0,48)$. For the second equation, the intercepts would be $(36,0)$ and $(0,36)$.

• I'm confused now.... – suomynonA Sep 20 '16 at 0:25
• Edited post with a graph – suomynonA Sep 20 '16 at 0:27
• @WilliamZlacki found the intercepts...isn't $144/8=18$? – suomynonA Sep 20 '16 at 0:28
• @WilliamZlacki ok, I was very confused for a bit... – suomynonA Sep 20 '16 at 0:34
• @WilliamZlacki What do you mean by that? I only used the four points I mentioned. – suomynonA Sep 20 '16 at 0:40