Question
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Last month, there were 4 sunny days for every rainy day. If there were 30 days in the month, how many days were rainy? Explain your reasoning. If you get stuck, consider using a tape diagram.

Ask by Rowe Gardner. in the United States
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

There were 6 rainy days in the month.

Solution

**Step 1: Define the variable** Let \( x \) be the number of rainy days. **Step 2: Express the number of sunny days** Since there were 4 sunny days for every rainy day, the number of sunny days is \( 4x \). **Step 3: Set up the equation** The total number of days in the month is given as 30. Therefore, the sum of rainy and sunny days is: \[ x + 4x = 30 \] **Step 4: Solve the equation** Combine like terms: \[ 5x = 30 \] Divide both sides by 5: \[ x = \frac{30}{5} = 6 \] **Step 5: Conclusion** There were \( 6 \) rainy days in the month.

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The Deep Dive

Let’s break it down! If there were 4 sunny days for every rainy day, you can think of this as a ratio of sunny to rainy days: 4 sunny days to 1 rainy day. This means for every 5 days total (4 sunny + 1 rainy), there’s a certain pattern. Now, if the month has 30 days, you can divide 30 by 5 to figure out how many sets of “4 sunny days and 1 rainy day” you have. That equals 6 sets (30 ÷ 5 = 6). So, if each set has 1 rainy day, you multiply the number of sets (6) by the rainy days per set (1), which gives you 6 rainy days in total! Got a visual thinker? A tape diagram would show 5 equal sections labeled 4 sunny and 1 rainy. Filling it in for 6 sets shows you clearly that you have 6 rainy days out of the month!

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