linear question

Question

 A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising it sells 250 units. For each additional $3000 spent, an additional 15 units are sold. 

a) How many units does the firm sell if it spends $25,000 on advertising? (do not include any commas in your answer) 

 

b) How many units does the firm sell if it spends $50,000 on advertising? (do not include any commas in your answer)

 

c) If 𝑥x is the amount of money that the company spends on advertising, find a formula for 𝑦y, the number of units sold as a function of 𝑥x. (Do not use commas in your formula). 

d) How much advertising money must be spent to sell 700 units? (do not include any commas in your answer) 

Answer 1

Let x = amount of money spent on advertising and y = number of units sold.

For a linear equation y = mx+b. From above, if no money is spent, x=0, then 250 units are sold,

so b = 250.

The slope, m, would be 15/3000 because for every $3000 spent, 15 more units are sold.

y = (15/3000)x + 250 = x/200 + 250

a) y(25000) = 25000/200 + 250 = 125 + 250 = 375 units

b) y(50000) = 50000/200 + 250 = 250 + 250 = 500 units

c) y = x/200 + 250 as derived above

d) 700 = x/200+250 Solve for x

x/200 = 450

x = 200(450) = $90000