Of the model cars manufactured in September, \(\frac{1}{5}\) were models of NASCAR cars and \(\frac{1}{3}\) were World War 2 vintage models. How many cars manufactured in September were neither NASCAR model cars nor World War 2 vintage model cars?
Answer (3)
Add 1/5 and 1/3. 1/3+1/5= First get common denominator( 15), So 5/15+3/15= 8/15 Then you calculate what is left over which is 7/15
This fraction represents the portion of total cars that do not belong to the specified categories.
To determine the number of cars that were neither NASCAR nor World War 2 vintage models in September, calculate the complement of the total of these two types of cars.
To determine how many model cars manufactured in September were neither NASCAR model cars nor World War 2 vintage model cars, let's analyze the information provided and use it to find a solution:
Fraction of NASCAR model cars : \( \frac{1}{5} \) of the total manufactured cars.
Fraction of World War 2 vintage model cars**: 3 1 of the total manufactured cars.
First, let's calculate the fraction of cars that were either NASCAR or World War 2 vintage models. We assume there is no overlap (no car that is both a NASCAR model and a WW2 vintage model), though this assumption wasn't explicitly stated.
Calculating the Combined Fraction
To combine the fractions, we'll add them:
Combined fraction = 5 1 + 3 1
We need a common denominator to add these fractions:
Common denominator = 15
5 1 = 15 3 and 3 1 = 15 5 C o mbin e df r a c t i o n = 15 3 + 15 5 = 15 8
Calculating the Fraction of Neither Type
The fraction of cars that are neither NASCAR models nor WW2 vintage models is:
Fraction neither = 1 − 15 8 = 15 7
So, 15 7 of the cars manufactured in September were neither NASCAR model cars nor World War 2 vintage model cars.
The fraction of cars manufactured in September that were neither NASCAR nor World War 2 vintage models is 15 7 . This means for every 15 cars, 7 were neither type. For 150 cars manufactured, that results in 70 cars being neither type.
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