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When the price is $\$ 50$ per radio, a producer will supply 100 radios each month for sale. For each $\$ 2$ increase in price the producer will supply an additional 6 radios. How many radios are supplied if their per unit price is $\$ 72 ?$

166

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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for this problem. We're gonna look at the number of radios that ah producer is providing Before we get into how this problem works. Let's record the information we know were given an initial, um, position. If I If the price point is $50 per radio, the producer will supply 100 radios to sell. Okay, so that's kind of our baseline $50 apiece means we're gonna have 100 radios to sell if I increase the price by $2. Okay, so I go from 50 to 52 from 52 to 54. Every time I increased the price by $2. That's gonna lead to an increase in the number of radios by six radios. So $50 is 100 radios. If I go up to 52 I go up to 106. If I go up to more to $54 I go up another six radios to 112 and so on. This is a linear relationship. As one goes up, the other goes up in a constant rate. So let's take a look at how many. Here's our question. How many radios will we have supplied to us. If the price is $72 there's my question. Okay, so let's take a look at what we have at our original price point. The number of radios, it's going to be 100. Okay, how does that change was going to go up? So we're gonna add some radios. Every time the price goes up by $2 we add some radios. So I want to know how many $2 increments by price has gone up. So what I'm going to do is I'm gonna look at the price minus that initial price point of 50. That will tell me the difference. So if my price is $60 a radio, that means I've gone up $10. 60 minus 50 to know how maney increments of two. I divide that number by two. So again, in my example, 60 minus 50 is 10 10, divided by two is five. It means I've gone up five increments of two. And for each of those increments by number of radios, goes up by six. So here's my, uh, formula. Now, let's try this for our specific example. Okay, again, we start with 100 radios. My price is $72. So I plugged that into my example here, 70 to minus 50 is 22. So my price has gone up $22 from that original price point that we were given $22 is 11 increments of two. And for each one of those 11 increments, I get six additional radios to sell, So in all I'm gonna have 166 radios to sell.

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