the total length of 4 blue banners and 5 yellow banners is 49 meters. the total length of 2 blue banners and 1 yellow banner is 17 meters all banners of the same color have the same length. find the length of each blue banner.
To find the length of each blue banner, we can set up a system of equations based on the given information.
Let's assume the length of each blue banner is "x" meters.
According to the first statement, the total length of 4 blue banners and 5 yellow banners is 49 meters. Since all blue banners have the same length, the total length of the blue banners would be 4 times the length of one blue banner, which is 4x meters. Similarly, the total length of the yellow banners would be 5 times the length of one yellow banner, which is 5y meters (where "y" represents the length of each yellow banner).
So, our first equation can be written as:
4x + 5y = 49 ----(1)
According to the second statement, the total length of 2 blue banners and 1 yellow banner is 17 meters. Hence, the total length of the blue banners would be 2 times the length of one blue banner, which is 2x meters. Similarly, the total length of the yellow banner would be 1 times the length of one yellow banner, which is 1y meters.
So, our second equation can be written as:
2x + 1y = 17 ----(2)
Now, we have a system of equations:
4x + 5y = 49 ----(1)
2x + 1y = 17 ----(2)
To solve this system of equations, we can use the method of substitution or elimination.
Using the method of substitution, we can rearrange equation (2) for "y" in terms of "x" as follows:
y = 17 - 2x ----(3)
Substitute equation (3) into equation (1) and solve for "x":
4x + 5(17 - 2x) = 49
4x + 85 - 10x = 49
-6x + 85 = 49
-6x = 49 - 85
-6x = -36
x = -36 / -6
x = 6
Therefore, the length of each blue banner is 6 meters.