Math Problem Statement

The bar chart below shows the number of evergreen trees and deciduous trees in three parks. Fern Park's bar is missing. The ratio of deciduous trees in North Park to deciduous trees in Fern Park is 2:1. The ratio of the total number of deciduous trees in the three parks to the total number of evergreen trees in the three parks is 2:3. Work out how many evergreen trees there are in Fern Park.

Solution

To solve this problem, we need to determine how many evergreen trees are in Fern Park based on the provided information.

Key Details and Relationships:

  1. Deciduous Trees Ratio (North Park to Fern Park):

    • The ratio is 2:1.
    • From the chart:
      • North Park has 8 deciduous trees.
      • Thus, Fern Park has 82=4\frac{8}{2} = 4 deciduous trees.
  2. Total Deciduous to Evergreen Tree Ratio:

    • The ratio of all deciduous trees to all evergreen trees is 2:32:3.

    • From the chart:

      • Total deciduous trees in the other parks are: 88 (North Park) + 1212 (Winter Park) + 44 (Fern Park) = 2424.
      • Let the total number of evergreen trees in all three parks be xx.

      Using the ratio 2:32:3, the relationship is: Total Deciduous TreesTotal Evergreen Trees=23.\frac{\text{Total Deciduous Trees}}{\text{Total Evergreen Trees}} = \frac{2}{3}. Substituting known values: 24x=23.\frac{24}{x} = \frac{2}{3}. Solving for xx: x=24×32=36.x = \frac{24 \times 3}{2} = 36. So, the total number of evergreen trees is 36.

  3. Breaking Down Evergreen Trees by Park:

    • From the chart:
      • North Park has 6 evergreen trees.
      • Winter Park has 14 evergreen trees.
    • Total evergreen trees in North and Winter Parks = 6+14=206 + 14 = 20.
    • Thus, the number of evergreen trees in Fern Park is: 3620=16.36 - 20 = 16.

Final Answer:

There are 16 evergreen trees in Fern Park.

Let me know if you'd like further clarification or have more questions! Here are some related questions for practice:

  1. How would the solution change if the ratio of deciduous to evergreen trees was 3:4 instead of 2:3?
  2. What is the total number of trees (deciduous + evergreen) in all three parks?
  3. How many more deciduous trees are there in Winter Park compared to Fern Park?
  4. If Fern Park had double the number of evergreen trees, what would the new total be?
  5. What is the percentage of deciduous trees in Winter Park relative to the total number of trees in Winter Park?

Tip: Always double-check ratios and totals for consistency to ensure accuracy in problem-solving!

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Math Problem Analysis

Mathematical Concepts

Ratios
Algebra
Proportional Reasoning

Formulas

Ratio of deciduous trees: Deciduous in North Park / Deciduous in Fern Park = 2 / 1
Total ratio formula: (Total Deciduous Trees / Total Evergreen Trees) = 2 / 3

Theorems

Ratio and Proportion Theorem

Suitable Grade Level

Grades 7-10