An advertising company charges $60 per half-page advertisement and $100 per full-page advertisement. michael has a budget of $1340 to purchase 15 advertisements. define a variable for each unknown. write a system of equations to represent the situation. how many half-page advertisements does michael purchase? show your work. how many full-page advertisements does michael purchase? show your work.4

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let the number of half page ads be represented by h

Let the number of full page ads be represented by f.

Total number of advertisements = 15

h + f = 15 ....... (i)

h = 15 - f

Therefore, the system of equations to represent the situation will be:

60h + 100f = 1340 ........ (ii)

Put the value of h into equation (ii)

60(15 - f) + 100f = 1340

[tex]\Rightarrow[/tex] 900 - 60f + 100f = 1340

Collect like terms

100f-60f = 1340-900

[tex]\Rightarrow[/tex] 40f = 440

[tex]\Rightarrow[/tex] f = 11

The number of full-page advertisements that Michael purchased is 11.

Since h + f = 15

[tex]\Rightarrow[/tex] h + 11 = 15

[tex]\Rightarrow[/tex] h = 15 - 11

[tex]\Rightarrow[/tex] h = 4

The number of half page advertisements that Michael purchased is 5.

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