A Television Commercial Announces A Certain Type Of Ba ✓ Solved
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 Instructions
The problem involves understanding the relationship between the lifespan of two types of batteries as presented in a commercial and using the given data to find the minimum required lifespan of the second battery for the claim to be valid. To address this, we will translate the problem into a mathematical equation and perform the necessary calculations step-by-step.
Understanding the Problem
The commercial states that the advertised battery lasts, on average, 20 hours longer than twice the lifespan of another battery. Mathematically, if we denote the lifespan of the second battery as x hours, then the lifespan of the advertised battery is expressed as:
Ladvertised = 2x + 20
According to consumer testing, the advertised battery lasts 725 hours. For the claim to be valid based on this test, the actual measured performance should at least be equal to the claimed average, i.e., 725 hours.
Setting up the Equation
Since the tested advertisement battery lasted 725 hours, the condition for the claim's validity can be expressed as:
725 ≥ 2x + 20
Solving for x
To find the minimum lifespan of the other battery (x), we will isolate x in the inequality:
- Subtract 20 from both sides: 725 - 20 ≥ 2x
- Simplify: 705 ≥ 2x
- Divide both sides by 2: 705 / 2 ≥ x
Calculating the right side:
x ≤ 352.5
Interpretation of the Result
The value x ≤ 352.5 hours indicates that for the commercial's claim to be valid based on the consumer tests showing 725 hours, the other type of battery must last at least 352.5 hours.
In conclusion, the minimum lifespan required for the other battery to support the commercial's claim is approximately 352.5 hours.
Additional Considerations
This calculation assumes that the tester's data accurately reflects the average performance and that the consumer test's duration is representative. Variance in battery performance and testing conditions could affect this, but based solely on the data provided, 352.5 hours is the critical threshold.
References
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