In a certain apartment building, the ratio of tenants to cars is 3:5. If there are 30 tenants, how many cars are there?
Understand the Problem
The question is asking for the number of cars in an apartment building based on the given ratio of tenants to cars, which is 3:5. With 30 tenants, we need to find out how this ratio translates into the number of cars.
Answer
The number of cars is \( C = 50 \).
Answer for screen readers
The number of cars is ( C = 50 ).
Steps to Solve
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Identify the ratio The ratio of tenants to cars is given as 3:5.
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Set up the equation Let the number of tenants be represented by ( T ) and the number of cars by ( C ). Based on the given ratio, we can write: $$ \frac{T}{C} = \frac{3}{5} $$
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Substitute the known value We know that there are 30 tenants, so we substitute ( T ) with 30: $$ \frac{30}{C} = \frac{3}{5} $$
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Cross-multiply to solve for cars Cross-multiplying gives us: $$ 3C = 150 $$
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Divide to find the number of cars Now, divide both sides by 3 to find ( C ): $$ C = \frac{150}{3} = 50 $$
The number of cars is ( C = 50 ).
More Information
In this context, with a ratio of 3:5, it means for every 3 tenants, there are 5 cars. This relationship allows us to easily calculate the number of cars based on the tenant count.
Tips
- A common mistake is misinterpreting the ratio. Ensure that the ratio is applied correctly, using the total number of tenants to find the corresponding number of cars.
- Another mistake might be miscalculating while cross-multiplying. Double-check math operations to avoid errors.
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