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There are 6049 trees planted side by side on one side of a highway, each of whic...
Mar 9, 2024
There are 6049 trees planted side by side on one side of a highway, each of which is a group of several adjacent trees, a total of 2016 groups, in which the first group has m trees, the last group has n trees, if there are 39 trees in any of the 13 groups of adjacent trees, then what is m+n=
Solution by Steps
step 1
First, we need to express the total number of trees in terms of the groups and the trees in the first and last group
step 2
The total number of trees is equal to the sum of trees in all groups. Since there are 2016 groups and 13 of these groups have 39 trees each, we can express the total as 6049=m+2016×39−13×39+n 6049 = m + 2016 \times 39 - 13 \times 39 + n
step 3
Simplify the equation by multiplying and subtracting the constants: 6049=m+78744−507+n 6049 = m + 78744 - 507 + n
step 4
Combine like terms to simplify further: 6049=m+78237+n 6049 = m + 78237 + n
step 5
Rearrange the equation to solve for n n in terms of m m : n=6049−78237−m n = 6049 - 78237 - m
step 6
Substitute the value of n n back into the equation to find m+n m + n : m+n=m+(6049−78237−m) m + n = m + (6049 - 78237 - m)
step 7
Simplify the equation to find m+n m + n : m+n=6049−78237 m + n = 6049 - 78237
step 8
Calculate m+n m + n : m+n=−72188 m + n = -72188
Answer
m+n=−72188 m + n = -72188
Key Concept
Solving a linear equation with two variables
Explanation
We used the given total number of trees and the information about the groups to set up a linear equation. By simplifying and rearranging the equation, we solved for n n in terms of m m and then found the sum m+n m + n .
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