Question

Thanks for the help, question below :)

Answer 1

(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

Answer 2

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

b: 5

c: 8

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!