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.
Why did the blue banners go on strike? They were tired of being measured all the time! But don't worry, I've got a solution for you! Let's solve this math puzzle together.
Let's assume the length of each blue banner is "x" meters.
According to the information given, the total length of 4 blue banners is 4x meters, and the total length of 5 yellow banners is 5y meters.
We know that the total length of 4 blue banners and 5 yellow banners is 49 meters, so we can write the equation:
4x + 5y = 49
Similarly, the total length of 2 blue banners and 1 yellow banner is 17 meters, so we can write the equation:
2x + y = 17
Now, we have a system of equations that we can solve to find the length of each blue banner.
To make things simpler, let's solve the second equation for "y":
y = 17 - 2x
Now we can substitute this value of "y" into the first equation:
4x + 5(17 - 2x) = 49
Simplifying this equation, we get:
4x + 85 - 10x = 49
-6x = -36
x = 6
So, each blue banner has a length of 6 meters.
Remember, math is no joking matter, but sometimes a little humor can make it more enjoyable!
Let's assume that the length of each blue banner is represented by the variable 'b', and the length of each yellow banner is represented by the variable 'y'.
From the given information, we can form two equations:
Equation 1: 4b + 5y = 49 (total length of 4 blue and 5 yellow banners is 49 meters)
Equation 2: 2b + y = 17 (total length of 2 blue and 1 yellow banners is 17 meters)
Since we want to find the length of each blue banner, we need to eliminate the variable 'y' from these equations.
Let's multiply Equation 2 by 5 to make the coefficients of 'y' in both equations cancel each other out:
5 * (2b + y) = 5 * 17
10b + 5y = 85
Now we have two equations:
Equation 1: 4b + 5y = 49
Equation 3: 10b + 5y = 85
To eliminate 'y' from these equations, we can subtract Equation 1 from Equation 3:
(10b + 5y) - (4b + 5y) = 85 - 49
10b - 4b + 5y - 5y = 36
6b = 36
b = 36 / 6
b = 6
Therefore, the length of each blue banner is 6 meters.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the length of each blue banner is "b" meters and the length of each yellow banner is "y" meters.
From the given information, we can create two equations:
Equation 1: 4b + 5y = 49
This equation represents the total length of 4 blue banners and 5 yellow banners being equal to 49 meters.
Equation 2: 2b + y = 17
This equation represents the total length of 2 blue banners and 1 yellow banner being equal to 17 meters.
Now we can solve this system of equations. There are multiple ways to do this, but let's use the substitution method.
From Equation 2, we can rearrange it to solve for y:
y = 17 - 2b
Now substitute this value of y into Equation 1:
4b + 5(17 - 2b) = 49
Simplifying this equation gives us:
4b + 85 - 10b = 49
-6b + 85 = 49
-6b = 49 - 85
-6b = -36
b = -36 / -6
b = 6
So, the length of each blue banner is 6 meters.
This is a simple problem of solving 2 equations with 2 unknowns:
1) 4blue + 5yellow = 49
2) 2blue + 1yellow = 17
Multiply equation 2) by 2:
2) 4blue + 2yellow = 34
Now, subtract 2) from 1):
(4blue + 5yellow) - (4blue + 2yellow) = 49 - 34;
3yellow = 15;
yellow = 5 meters
Substitute in equation 2)"
2blue + 5 = 17;
2blue = 12;
blue = 6 meters