Math Problem Statement

8) A wooden plank is 3 meters long. The plank is cut into 8 equal pieces. What is the length of each piece? 9) If a recipe calls for 2 cups of flour to make 12 cookies, how many cups of flour would you need to make 30 cookies? 10) What is the median value of the following values: $808, $1258, $658, $1258, $900, $1358, $960, and $852?

Solution

Let's solve each question one by one:

Question 8

A wooden plank is 3 meters long. The plank is cut into 8 equal pieces. What is the length of each piece?

To find the length of each piece, divide the total length by the number of pieces: Length of each piece=3 meters8=0.375 meters\text{Length of each piece} = \frac{3 \text{ meters}}{8} = 0.375 \text{ meters} Answer: C) 0.375

Question 9

If a recipe calls for 2 cups of flour to make 12 cookies, how many cups of flour would you need to make 30 cookies?

We can set up a proportion to solve this: 2 cups12 cookies=x cups30 cookies\frac{2 \text{ cups}}{12 \text{ cookies}} = \frac{x \text{ cups}}{30 \text{ cookies}} Cross-multiply to solve for xx: 2×30=12×x60=12xx=6012=5 cups2 \times 30 = 12 \times x \Rightarrow 60 = 12x \Rightarrow x = \frac{60}{12} = 5 \text{ cups} Answer: 5 cups of flour

Question 10

What is the median value of the following values: $808, $1258, $658, $1258, $900, $1358, $960, and $852?

To find the median, we first arrange the values in ascending order: 658,808,852,900,960,1258,1258,1358658, 808, 852, 900, 960, 1258, 1258, 1358 Since there are 8 values (an even number), the median will be the average of the 4th and 5th values: Median=900+9602=18602=930\text{Median} = \frac{900 + 960}{2} = \frac{1860}{2} = 930 Answer: $930


Would you like a more detailed explanation for any of these answers, or do you have additional questions?

Here are some follow-up questions based on these problems:

  1. How would you find the length of each piece if the plank were divided into 12 pieces instead?
  2. If you wanted to make 24 cookies, how much flour would you need?
  3. How would you calculate the mean (average) value of the amounts given in Question 10?
  4. What would the median be if there were an additional value of $700 added to the list in Question 10?
  5. Can you find the mode of the amounts listed in Question 10?

Tip: For median calculations, always ensure the values are sorted in ascending order first!

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Math Problem Analysis

Mathematical Concepts

Division
Ratios and Proportions
Statistics

Formulas

Division formula: Total ÷ Number of parts
Proportion: (a/b) = (c/d)
Median calculation for ordered data

Theorems

Proportion theorem
Median calculation rule for even set of numbers

Suitable Grade Level

Grades 6-8