Question

Mugs Café sells 1000 cups of coffee per week if it does not advertise. For every $50 spent in advertising per week, it sells an additional 150 cups of coffee. a) Find a linear function that gives y = number of cups of coffee sold per week x = amount spent on advertising per week. b) How many cups of coffee does Mugs Café expect to sell if $100 per week is spent on advertising?

Answer 1

1,300 cups

Step-by-step explanation:

This can be solved as follows:

Question "a"

y = a + bx ................................................. (1)

Where,

y = number of cups of coffee sold per week

x = number of times b is multiplied based on the amount spent on adverts

amount spent on advertising per week

a = fixed cups of coffee per week without advertising = 1,000 cups

b = extra quantity sold when $50 is spent on advertisement = 150 cups

If the available figures above are substituted into equation (1), we will have the linear function as follows:

y = 1000 + 150x ................................................. (2)

Equation (2) is the linear function required.

Question "b"

If $100 per week is spent on advertising, we can get X by dividing it by $50 as follows:

x = $100 ÷ $50 = 2

Substituting 2 for x in equation (2), we can calculate y as follows:

y = 1000 + 150(2)

= 1000 + 300

= 1,300 cups.

Therefore, 1,300 cups of coffee are expected to be sold per week by Mugs Café if it spends $100 per week on advertising.

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