### Problem Statement:**In Lee Middle School, the ratio of the number of fifth-graders to the number of sixth-graders is 5 to 4, and there are 16 more fifth-graders. If the ratio of the number of sixth-graders to the number of seventh-graders is 2 to 3, what is the mean number of students in the three grades?**---**Your Answer:**[Text Box for User Input] ---### Explanation:In this problem, we need to find the mean number of students in the fifth, sixth, and seventh grades given the following ratios and information:1. The ratio of fifth-graders to sixth-graders is 5:4.2. There are 16 more fifth-graders than sixth-graders.3. The ratio of sixth-graders to seventh-graders is 2:3.Here's how to solve this step-by-step:1. **Set up the ratios using variables:** - Let the number of sixth-graders be $ 4x $. - Hence, the number of fifth-graders is $ 5x $ (since the ratio is 5:4).2. **Account for the additional 16 fifth-graders:** \[ 5x = 4x + 16 \] Solve for $ x $: \[ x = 16 \]3. **Calculate the actual number of fifth and sixth graders:** - Sixth-graders: $ 4x = 4 \cdot 16 = 64 $ - Fifth-graders: $ 5x = 5 \cdot 16 = 80 $4. **Use the second ratio to find the number of seventh-graders:** - The ratio of sixth-graders to seventh-graders is 2:3. - If the number of sixth-graders is 64 (which is $ 2y $), then the number of seventh-graders is $ 3y $. - Setting $ 2y = 64 $, we get $ y = 32 $. Number of seventh-graders: \[ 3y = 3 \cdot 32 = 96 \]5. **Calculate the mean number of students:** - Total number of students: \( 80 + 64 + 96 =

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Description: ### Problem Statement:**In Lee Middle School, the ratio of the number of fifth-graders to the number of sixth-graders is 5 to 4, and there are 16 more fifth-graders. If the ratio of the number of sixth-graders to the number of seventh-graders is 2 t

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In Lee Middle School, the ratio of the number of fifth-graders to the number of sixth-graders is 5 to 4, and there are 16 more fifth-graders. If the ratio of the number of sixth-graders to the number of seventh-graders is 2 to 3, what is the mean number of students in the three grades? Your Answer:

In Lee Middle School, the ratio of the number of fifth-graders to the number of sixth-graders is 5 to 4, and there are 16 more fifth-graders. If the ratio of the number of sixth-graders to the number of seventh-graders is 2 to 3, what is the mean number of students in the three grades? Your Answer:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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