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.
4B+5Y=49
2B+1Y=17
multipy the second equation by 2, and subtract.
3Y=15
y=5
then B=6
check my work
Let's denote the length of a blue banner as 'x' and the length of a yellow banner as 'y'.
From the given information:
4x + 5y = 49 (Equation 1)
2x + y = 17 (Equation 2)
To find the length of each blue banner (x), we need to solve these two equations.
First, we can rearrange Equation 2 to express y in terms of x:
y = 17 - 2x (Equation 3)
Now, substitute this expression for y into Equation 1:
4x + 5(17 - 2x) = 49
Simplify and solve for x:
4x + 85 - 10x = 49
-6x = -36
x = 6
Therefore, each blue banner has a length of 6 meters.
Let's start by assigning variables to the unknowns. Let's say the length of each blue banner is "b" meters, and the length of each yellow banner is "y" meters.
According to the information given, we know that:
4 blue banners + 5 yellow banners = 49 meters -- Equation 1
2 blue banners + 1 yellow banner = 17 meters -- Equation 2
We can solve this system of equations using the method of substitution.
Let's solve Equation 2 for "y" in terms of "b":
2b + y = 17 => y = 17 - 2b -- Equation 3
Now, substitute the value of "y" from Equation 3 into Equation 1:
4b + 5(17 - 2b) = 49
Simplify the equation:
4b + 85 - 10b = 49
-6b = 49 - 85
-6b = -36
Divide by -6:
b = -36 / -6
b = 6
Therefore, the length of each blue banner is 6 meters.