Question

Mr. Boyle is restocking the gym for 2017 and needs to buy a total of 8 new balls for the gym. At a sports store, basketballs cost $20 each and footballs cost $15. If Mr. Boyle is prepared to spend up to $150, what is a possible number of footballs and basketballs that he can buy? Use the coordinate grid to support your answer. Then, in at least 5 sentences, explain how you arrived at your answer.

Answer 1

Start by naming the variables

x= basketballs

y=footballs

write the system of equations

`x+y=8`

also when he says up to means that the cost can be less or equal to 150

`20x+15y\leq150`

continue by graphing both of the equations

He could buy 6 basketballs and 2 footballs in order to spend $150

The black line represents the amount of balls Mr. Boyle needs, each point that lies on this line is a possible combination of how to buy the balls, the blue shaded region represents all the combinations that will cost less than $150, the point (6,2) is the maximim combination he can use.