Use a variation model to solve for the unknown value. Some...

Use a variation model to solve for the unknown value. Some body-builders claim that, within safe limits, the number of repetitions that a person can complete on a given weight-lifting exercise is inversely proportional to the amount of weight lifted. Roxanne can bench press 45 lb for 15 repetitions. a. How many repetitions can Roxanne bench with 60 lb of weight? b. How many repetitions can Roxanne bench with 75 lb of weight? c. How many repetitions can Roxanne bench with 100 lb of weight?

Use a variation model to solve for the unknown value.
Some body-builders claim that, within safe limits, the number of repetitions that a person can complete on a given weight-lifting exercise is inversely proportional to the amount of weight lifted. Roxanne can bench press 45 lb for 15 repetitions.
a. How many repetitions can Roxanne bench with 60 lb of weight?
b. How many repetitions can Roxanne bench with 75 lb of weight?
c. How many repetitions can Roxanne bench with 100 lb of weight?

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Key Concepts

Constant of Variation

In problems involving inverse relationships, the constant of variation is the fixed product of the two quantities involved. Once this constant is determined from known values, it can be used to calculate unknown values when one of the quantities changes. This technique is central to solving inverse variation equations.

Mathematical Modeling

Mathematical modeling is the process of translating real-world scenarios into mathematical expressions or equations. By using a variation model, one creates an equation based on the inverse proportionality between two variables, which then can be solved to find unknown values. This method is widely used to analyze and predict outcomes in various fields, including physics, economics, and health sciences.

Inverse Proportionality

This concept refers to a relationship where one variable increases as the other decreases, such that their product remains constant. It is a fundamental idea used to model situations where a change in one quantity inversely affects another, making it essential for solving problems that involve balancing competing effects.

Transcript

00:03 So the question is asking about the number of the reps a person can complete is inversely proportioned to the amount lifted.

00:09 If a person can lift 45 pounds for 15 reps, how many reps can they do as 60 pounds, 75 pounds, and 100 pounds? so we're going to use the information they gave us.

00:19 We have 45 pounds for 15 reps.

00:22 With that information, then, we can write our proportion of 45 over 15.

00:26 That should be equal to, for our first one, we have 60 pounds.

00:30 So that's going to be 60 over x because that's what we're saying.

00:33 Selling for how many reps can they do.

00:35 We're then going to go ahead and we're going to cross multiply.

00:38 So we're going to multiply our 15 times or 60 and our x times are 45.

00:41 So we end up with 45x is going to be equal to 900.

00:46 Now we have to solve our x, getting rid of what's connected to it.

00:50 45 is being multiplied.

00:51 So we're going to divide by 45 on both sides.

00:54 When we do that, x is now by yourself and it's going to be equal to 20 reps.