Math  /  Algebra

Question10 Multiple Choice 1 point In a parking garage, there are 5 cars for every 4 SUVs. Based on this ratio, how many cars and SUVs could be in the parking garage? 80 SUVs and 64 cars 72 SUVs and 90 cars 25 SUVs and 15 cars 84 SUVs and 126 cars

Studdy Solution

STEP 1

What is this asking? Which of these options keeps the same proportion of cars to SUVs as 5 cars to every 4 SUVs? Watch out! Don't mix up the cars and SUVs!
Make sure you're comparing the right numbers.

STEP 2

1. Set up the proportion.
2. Check the options.

STEP 3

We know the **basic ratio** is 5 cars for every 4 SUVs.
We can write this as a fraction: 5 cars4 SUVs\frac{5 \text{ cars}}{4 \text{ SUVs}}.
This is our **target ratio**!

STEP 4

Let's see if 64 cars80 SUVs\frac{64 \text{ cars}}{80 \text{ SUVs}} matches our **target ratio**.
We can simplify this fraction by dividing both the top and bottom by their **greatest common divisor**, which is 16.
So, 6480=64÷1680÷16=45\frac{64}{80} = \frac{64 \div 16}{80 \div 16} = \frac{4}{5}.
This is *not* the same as our **target ratio** 54\frac{5}{4}.

STEP 5

Does 90 cars72 SUVs\frac{90 \text{ cars}}{72 \text{ SUVs}} match our **target ratio**?
Dividing both numbers by their **greatest common divisor**, 18, gives us 9072=90÷1872÷18=54\frac{90}{72} = \frac{90 \div 18}{72 \div 18} = \frac{5}{4}.
This *matches* our **target ratio**!

STEP 6

Let's check 15 cars25 SUVs\frac{15 \text{ cars}}{25 \text{ SUVs}}.
Dividing both by 5 gives us 1525=15÷525÷5=35\frac{15}{25} = \frac{15 \div 5}{25 \div 5} = \frac{3}{5}.
Nope, not the same as our **target ratio**.

STEP 7

Finally, let's look at 126 cars84 SUVs\frac{126 \text{ cars}}{84 \text{ SUVs}}.
Dividing by the **greatest common divisor**, 42, we get 12684=126÷4284÷42=32\frac{126}{84} = \frac{126 \div 42}{84 \div 42} = \frac{3}{2}.
This doesn't match our **target ratio** either.

STEP 8

The correct answer is 72 SUVs and 90 cars!

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