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There are 53 major sources of pollen in state A. These pollen sources are categorized as grasses, weeds, and trees. If the number of weeds is 9 less than twice the numb of grasses, and the number of trees is 2 more than twice the number of grasses, find the number of grasses, weeds, and trees that are major pollen sources. The number of grasses in state A is 12 . The number of weeds in state A is

Ask by Perkins Curry. in the United States
Feb 04,2025

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Answer

The number of weeds in state A is 15.

Solution

Given: - Total major pollen sources: 53 - Categories: Grasses (G), Weeds (W), Trees (T) You've already determined that: - **Number of grasses (G) = 12** Using the relationships provided: 1. **Weeds (W)** are 9 less than twice the number of grasses: \[ W = 2G - 9 = 2(12) - 9 = 24 - 9 = 15 \] 2. **Trees (T)** are 2 more than twice the number of grasses: \[ T = 2G + 2 = 2(12) + 2 = 24 + 2 = 26 \] **Summary of Major Pollen Sources in State A:** - **Grasses:** 12 - **Weeds:** 15 - **Trees:** 26 These numbers add up to the total: \[ 12\ (\text{Grasses}) + 15\ (\text{Weeds}) + 26\ (\text{Trees}) = 53 \] **Answer:** The number of weeds in state A is 15.

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To find the number of weeds, we can use the information provided. The number of weeds is stated to be 9 less than twice the number of grasses. Given that the number of grasses is 12, we can set up the following equation for weeds: Weeds = 2 * Grasses - 9 Weeds = 2 * 12 - 9 Weeds = 24 - 9 Weeds = 15 Therefore, the number of weeds in state A is 15. Now, let's calculate the number of trees using the information given. The number of trees is 2 more than twice the number of grasses: Trees = 2 * Grasses + 2 Trees = 2 * 12 + 2 Trees = 24 + 2 Trees = 26 Thus, the total pollens sources are: - Grasses: 12 - Weeds: 15 - Trees: 26 When we add them up, we have: 12 (Grasses) + 15 (Weeds) + 26 (Trees) = 53, confirming the total count is correct!

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