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Home » 4/3 = 16/x. - Dachbleche24

4/3 = 16/x. - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 4Dr. Emily Carter returned to the fossil site and found a layered deposit. The top layer contains 45 fossilized fern fronds, the middle has twice as many, and the bottom layer has 30 fewer than the sum of the top two layers. If each frond represents one plant, what is the total number of fossil plants across all layers?

📌 Mid layer: 2 × 45 = <<2 × 45 = 90>>90

📌 Sum of top two: 45 + 90 = <<45 + 90 = 135>>135

📌 Bottom layer: 135 - 30 = <<135 - 30 = 105>>105

📌 Total: 45 + 90 + 105 = <<45 + 90 + 105 = 240>>240

📌 5Dr. Liam Chen is comparing artifact distributions in 4 villages. Village populations were 180, 240, 300, and 360. He wants to divide each village into clans with the same number of members, minimizing clan size while maximizing uniformity. What is the largest possible clan size that divides all four populations exactly?

📌 Find GCD of 180, 240, 300, 360

📌 GCD(180,240) = 60

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The \( n \)-th term is given by \( a_n = a + (n-1)d \).
Use \( n = 15 \): \( a_{15} = 3 + (15-1) \times 4 \).
Simplify: \( a_{15} = 3 + 14 \times 4 = 3 + 56 = 59 \).
Therefore, the 15th term is 59.
#### 59
The ratio of the number of apples to oranges in a basket is 5:3. If th...
Let the number of oranges be \( x \). The ratio equation is \( \frac{4...
Cross-multiply: \( 5x = 3 \times 40 \).
Solve for \( x \): \( 5x = 120 \).
Divide by 5: \( x = 24 \).

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