Tutor profile: Rebecca A.
A flagpole is mounted on the front of a library's roof. From a point 100ft in front of the library, the angles of elevation to the base of the flagpole and the top of the flag pole are 28 degrees and 39 degrees respectively. Find the height of the flagpole.
The sum of two numbers is 26. The second number is one less than two times the first number. What are the two numbers?
Step one: Create variable names for each number. Let's use x and y. We know the sum of these two numbers is 26, therefore we know, x+y=26. The problem also told us that "the second number is one less than two times the first number" therefore we can write the equation y=2x-1. This gives us two equations that we can put into a system to solve. There are multiple ways to solve this system, but I will use substitution. I will substitute the equation y=2x-1 into the y value in the equation x+y=26. Doing this substitution gives us the new equation x+(2x-1)=26. This simplifies to 3x-1=26. Solving for x gives us x=9. After substituting x=9 into the equation x+y=26. we find y= 17. Therefore the two numbers that satisfy the problem are 9 and 17.
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