Question

A local retailer has determined that the number of Porta Boy game systems sold in a week is related to the price in dollars of each system. 40 game systems were sold when the price was $120. When the systems went on sale the following week, 100 systems were sold at $75 each. (a) Find a linear equation which fits this data. Use the weekly sales as the input variable and the price as the output variable. Answer: y = -5x + 320 (b) If the retailer wants to sell 140 PortaBoys next week, what should the price be? Answer: $180

          A local retailer has determined that the number of Porta Boy game systems sold in a week is related to the price in dollars of each system. 40 game systems were sold when the price was $120. When the systems went on sale the following week, 100 systems were sold at $75 each.

(a) Find a linear equation which fits this data. Use the weekly sales as the input variable and the price as the output variable. Answer: y = -5x + 320

(b) If the retailer wants to sell 140 PortaBoys next week, what should the price be? Answer: $180
        
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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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A local retailer has determined that the number of Porta Boy game systems sold in a week is related to the price in dollars of each system. 40 game systems were sold when the price was $120. When the systems went on sale the following week, 100 systems were sold at $75 each. (a) Find a linear equation which fits this data. Use the weekly sales as the input variable and the price as the output variable. Answer: y = -5x + 320 (b) If the retailer wants to sell 140 PortaBoys next week, what should the price be? Answer: $180
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Transcript

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00:01 So a local retailers determine the number of games sold in a week is related to its price, or determines the price.
00:08 So we have 40 games systems sold when the price was 120.
00:12 So we're going to have 120 would be my price and my games would be 40.
00:19 So this needs to be reversed because they're talking about the games being dependent upon the price.
00:25 So my price is going to be my independent variable.
00:28 So i'm going to put it this direction.
00:30 And now it says 100 systems were sold, so that's going to be when the price was 75.
00:42 So we had 100 here.
00:44 We want to find the linear equation.
00:47 So we're going to go y equals mx plus b.
00:50 So i'm going to find my slope.
00:52 So i'm going to say 40 minus 100, that's negative 60, 120 minus 75.
00:58 That's going to be 45.
01:00 So that's going to be my slope then.
01:02 It's going to be negative 60 over 45.
01:06 I can reduce that by dividing by 15 to get negative 4 over 3.
01:12 So i'm going to say y equals negative 4 thirds x plus b, where x is my price...
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