Question

Thanks for the help, question below :)

Answer 1

Answer:

a: $40h+75f=800,h+f=13$

b: 5

c: 8

Step-by-step explanation:

Explanation for a: Making the equations

Assuming h is the amount of half-page ads and f is the amount of full page ads, we can create the equations $40h+75f=800,h+f=13$ since the total cost will be 800$, and we have a total of 13 ads.

Explanation for b: Solving for h

We can now solve for one of the variables using elimination. Let’s multiply the expression $h+f=13$ by -75.

$-75h - 75f = -975$

Great! Now let’s add the equations.

$40h + 75f = 800\\\\-75h - 75f = -975$

Adding these equations, we get

$-35h = -175$

Divide both sides by -35, and we get $h = 5$.

Explanation for c: Solving for f

We can now substitute h inside the equation $h + f = 13$.

$5 + f = 13\\\\f = 13-5\\\\f = 8$

Hope this helped!

Answer 2

(a) Let's say that h = half-page advertisement, and f = full-page advertisement.

Now It is given that there is a total of 13 advertisements present, and hence we have the first equation h + f = 13. Respectively we have the equation 40h + 75f = 800. This is represented by the following system of equations,

$\begin{bmatrix}h+f=13\\ 40h+75f=800\end{bmatrix}$

(c) From here on let's solve this system for h and f. Isolating h in the first equation would give us h = 13 - f, which then can be substituted into the second equation to receive 40(13 - f) + 75f = 800. Let's solve for f --- (1)

40(13 - f) + 75f = 800,

520 - 40f + 75f = 800,

520 + 35f = 800,

35f = 280,

f = 280 / 35 = 8 full advertisements

(b) Now let's substitute this value of f back into the first equation to solve for the value of h --- (2)

h + 8 = 13,

h = 13 - 8 = 5 half advertisements