A Television Commercial Advertises A Certain Type Of Bar

A Television Commercial Advertises That A Certain Type of Battery Will

A television commercial advertises that a certain type of battery will last, on the average, 20 hours longer than twice the life of another type of battery. If consumer tests show that the advertised battery lasts 725 hours, how many hours must the other type of battery last for the advertiser’s claim to be valid? (SHOW COMPLETE WORK)

Paper For Above instruction

The problem involves understanding the relationship between the durations of two different types of batteries as advertised in a commercial. The key information is that the advertised battery's lifespan is on average 20 hours longer than twice the lifespan of the other battery. The goal is to determine the minimum lifespan of the other battery's type that would validate the advertiser's claim, given the observed lifespan of the advertised battery.

Let’s define variables to represent the unknown quantities. Let x denote the lifespan in hours of the other type of battery. According to the problem, the advertised battery's lifespan is on average 20 hours longer than twice x, which can be mathematically expressed as:

Advertised Battery Lifespan = 2x + 20

Given that consumer tests show the advertised battery lasts 725 hours, we can set:

725 = 2x + 20

Now, solving for x involves isolating it on one side of the equation. Subtract 20 from both sides:

725 - 20 = 2x

705 = 2x

Next, divide both sides by 2:

x = 705 / 2 = 352.5

Thus, for the advertisement's claim to be valid, the other type of battery must last at least 352.5 hours on average. If the actual lifespan of that battery is less than this, then the claim that the advertised battery lasts 725 hours on average would not be supported by the relationship described in the advertisement.

Conclusion

The minimum lifespan of the other type of battery necessary to validate the commercial's claim, based on the observed 725 hours lifespan of the advertised battery, is approximately 352.5 hours. This calculation underscores the importance of understanding the mathematical relationship described in advertising claims and how it can be validated through basic algebraic techniques.

References

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