Direct Variation Question 2 with Solutions

Last week, I went over direct variation, and I gave you three direct variation problems to try on your own. You can see that post here: Direct Variation

Today I would like to give a solution to the second of those three problems. You can see solutions to the first problem here: Direct Variation Q1.

Example: The amount of revenue that an online magazine retailer makes in a month is directly proportional to the number of active subscribers to the magazine. In July, the magazine had a total of 1200 subscribers, and the retailer reported revenue of $7200. In August, the online magazine had a total of 1500 subscribers. How much revenue did the retailer make?

Try to solve the problem yourself before checking the solutions below.

Solutions: 

(1) Since the revenue, R, is directly proportional to the number of subscribers, x, R = kx for some constant k. We are given that R = 7200 when x = 1200, so that 7200 = k(1200), or k = 7200/1200 = 6. Thus, y = 6x. When x = 1500, we have y = 6 ⋅ 1500 = 9000.

(2) Since R is directly proportional to x,  R/x  is a constant. So we get the following ratio:  7200/1200 = R/1500. Cross multiplying gives 1200R = 7200 ⋅ 1500, or equivalently, R = (7200⋅1500)/1200 = 9000.

(3) The graph of R = f(x) is a line passing through the points (0, 0) and (1200, 7200). The slope of this line is  (7200 – 0)/(1200 – 0) = 6. Writing the equation of the line in slope-intercept form we have y = 6x. As in solution 1, when x = 1500, we have y = 6 ⋅ 1500 = 9000.

More Problems with Explanations

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