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 about finding the number of cars in relation to the number of tenants, given a specific ratio. To solve this, we can set up a proportion based on the ratio of tenants to cars, where 3 corresponds to the number of tenants and 5 corresponds to the number of cars.
Answer
The number of cars is \( 50 \).
Answer for screen readers
The number of cars is ( 50 ).
Steps to Solve
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Set up the ratio We know the ratio of tenants to cars is ( \frac{3}{5} ). This means for every 3 tenants, there are 5 cars.
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Create a proportion We can use the number of tenants given: 30. We set up the proportion as follows: $$ \frac{3}{5} = \frac{30}{x} $$ where ( x ) is the number of cars.
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Cross-multiply Now we will cross-multiply to solve for ( x ): $$ 3x = 5 \cdot 30 $$
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Calculate the right side Carrying out the multiplication: $$ 3x = 150 $$
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Solve for ( x ) To find ( x ), divide both sides by 3: $$ x = \frac{150}{3} $$
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Final calculation Thus, $$ x = 50 $$
The number of cars is ( 50 ).
More Information
In this problem, the ratio of tenants to cars helps to establish a straightforward proportion to find the missing value. Ratios like these are common in real-life scenarios, such as determining resources based on population.
Tips
- Misinterpreting the ratio: Ensure the ratio is consistently applied, not inverted.
- Failing to cross-multiply correctly: Check that both sides of the equation are accurately calculated.
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