An appliance store knows that if it sells its new gadgets for R 50 each it can sell 200 per month, and if it sells the same gadgets for R40, it will sell 300 per month. Let \( p \) represent the price of the gadgets and let \( n \) represent the number of gadgets that is sold per month. Assume that the relationship between price and sales is linear and that the sales are dependent on the price of the gadgets. The linear equation you could use to predict sales for other prices, is Select one: a. \( 10 p+n=700 \). b. \( 10 p-n=200 \). c. \( 10 p-n=700 \). (d. \( 10 p+n=600 \).

To determine the linear equation, we first establish the relationship between price (p) and the number of gadgets sold (n). We have two points: (50, 200) and (40, 300). The slope (m) can be calculated as: \( m = \frac{n_2 - n_1}{p_2 - p_1} = \frac{300 - 200}{40 - 50} = -10. \) Using the point-slope form of a line and rearranging, we end up with the equation \( n = -10p + 700 \). Thus, the equation can be rewritten as \( 10p + n = 700 \). So the correct answer is (a) \( 10 p+n=700 \). Another fun fact: Linear relationships like this one are not just applicable to gadgets—they can be seen in everyday life! For instance, think of your favorite lemonade stand: the number of cups sold might change depending on price. If the stand goes up to $2, they might sell fewer cups, but if it's just $1, they could sell out quickly. Understanding these dynamics is key to optimizing sales in any business! By the way, if you’re into diving deeper, you might want to explore some economic theories like the Law of Demand. It’s all about the relationship between price and demand, showing the inverse correlation most of the time—it’s fascinating to see hands-on how pricing strategies can greatly affect sales!