The ratio of the number of long term parking spaces to the number of short term parking spaces at Farmington airport is 5 to 7. the ratio of the number of short term parking spaces to the number of parking spaces in the cell phone lot is 8 to 9. if there are 3180 parking spaces at the airport, how many are in the cell phone lot?


To solve this problem, we can break it down step by step using the given ratios and total number of parking spaces.

### Step 1: Define Variables
Let:
- \( L \) represent the number of long-term parking spaces.
- \( S \) represent the number of short-term parking spaces.
- \( C \) represent the number of parking spaces in the cell phone lot.

We are given two ratios:
1. The ratio of long-term to short-term parking spaces is \( 5:7 \), which means:
   \[
   \frac{L}{S} = \frac{5}{7}
   \]
   So, \( L = \frac{5}{7}S \).

2. The ratio of short-term parking spaces to cell phone lot parking spaces is \( 8:9 \), which means:
   \[
   \frac{S}{C} = \frac{8}{9}
   \]
   So, \( S = \frac{8}{9}C \).

### Step 2: Total Number of Parking Spaces
We are told there are 3180 parking spaces in total, meaning:
\[
L + S + C = 3180
\]

### Step 3: Substituting the Ratios into the Total
From the ratios, we have:
\[
L = \frac{5}{7}S \quad \text{and} \quad S = \frac{8}{9}C
\]
Substitute \( S = \frac{8}{9}C \) into \( L = \frac{5}{7}S \):
\[
L = \frac{5}{7} \times \frac{8}{9}C = \frac{40}{63}C
\]

Now substitute both \( L \) and \( S \) in terms of \( C \) into the total equation:
\[
\frac{40}{63}C + \frac{8}{9}C + C = 3180
\]

### Step 4: Simplify the Equation
To simplify, find a common denominator for the fractions. The least common denominator for 63 and 9 is 63:
\[
\frac{40}{63}C + \frac{56}{63}C + \frac{63}{63}C = 3180
\]

Now combine the terms:
\[
\frac{40 + 56 + 63}{63}C = 3180
\]
\[
\frac{159}{63}C = 3180
\]

### Step 5: Solve for \( C \)
Multiply both sides by 63 to eliminate the denominator:
\[
159C = 3180 \times 63
\]
\[
159C = 200340
\]

Now divide both sides by 159:
\[
C = \frac{200340}{159} = 1260
\]

### Conclusion:
There are **1260** parking spaces in the cell phone lot.

---

Would you like a breakdown of any specific step, or do you have questions? Here are 5 related problems:

1. What if the total number of parking spaces was 5000, how many would be in the cell phone lot?
2. If the ratio of long-term to short-term parking spaces changed to 3:4, how would that affect the result?
3. What is the percentage of parking spaces in the cell phone lot compared to the total?
4. Can you find the number of long-term parking spaces at the airport?
5. How many short-term parking spaces are at the airport?

**Tip:** Always check your ratios carefully when substituting into equations, as small errors can lead to larger mistakes.

The ratio of the number of long term parking spaces to the number of short term parking spaces at Farmington airport is 5 to 7. The ratio of the number of short term parking spaces to the number of parking spaces in the cell phone lot is 8 to 9. If there are 3180 parking spaces at the airport, how many are in the cell phone lot?

Learn how to solve a ratio-based parking problem at Farmington Airport, where the total number of parking spaces is 3180. Using ratios between long-term, short-term, and cell phone lot spaces, we break down the solution step-by-step. Perfect for students in Grades 8-10.

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