Question

4) Math Club members want to advertise their fundraiser each week in the school paper. They knowthat a front-page ad is more effective than an ad inside the paper. They have a $30 advertisingbudget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertiseat least 20 times. a) Write and graph a system of inequalities to model the number of advertisements the club canpurchase to stay under budget. Be sure to label all parts of your graph.b) State one solution that would work. How much money will remain in the club's budget?

Answer 1

Problem:

Math Club members want to advertise their fundraiser each week in the school paper. They know that a front-page ad is more effective than an ad inside the paper. They have a $30 advertising budget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertise at least 20 times.

a) Write and graph a system of inequalities to model the number of advertisements the club can purchase to stay under budget. Be sure to label all parts of your graph.

Solution:

Let us denote the number of front-page ads by x, and the number of inside ads by y:

x = number front-page ads

y= number of inside ads

Now, because they have a $30 advertising budget and It cost $2 for each front-page ad and $1 for each inside page ad, the first inequality that we have is:

`2x+\text{ y }\leq30`

If we represent the graph of the equality (line) 2x+y = 30, we have:

On the other hand, because the club wants to advertise at least 20 times, the second inequality that we have is:

`x+y\ge20`

If we represent the graph of the equality (line) x+y = 20, we have:

Now, the intersection point of the above lines, that is 2x+y = 30 and x+y = 20 is found as follows:

we have

y = 30 - 2x

and

y = 20-x

then

30-2x = 20-x

and

30-20 = 2x-x

that is

10 = x

when x = 10 then y = 20-x = 20-10 = 10