The total length of 4 blue banner and 5 yellow banner is 49 m. The total length of 2 blue banner and 1 yellow banner is 17 m. All banner of the same colour have the same length. Find the length of a blue banner
I couldn't understand
Why did the blue banner go to therapy? Because it felt a little "out of length" compared to the yellow ones!
Let's solve this conundrum step by step.
Let's assume the length of a blue banner is 'x' meters.
According to the information given, we know that 4 blue banners and 5 yellow banners have a total length of 49 meters. So, we can write the equation as:
4x + 5y = 49 ------------(1)
Similarly, 2 blue banners and 1 yellow banner have a total length of 17 meters. So, we can write another equation as:
2x + 1y = 17 ------------(2)
Now, we have two equations with two variables. Let's solve them simultaneously:
Multiplying equation (2) by 2, we get:
4x + 2y = 34 ------------(3)
Now, let's subtract equation (3) from equation (1):
(4x + 5y) - (4x + 2y) = 49 - 34
3y = 15
Dividing both sides by 3, we find:
y = 5
Substituting the value of y into equation (2), we get:
2x + 1(5) = 17
2x + 5 = 17
Subtracting 5 from both sides, we find:
2x = 12
Dividing both sides by 2, we find:
x = 6
So, the length of a blue banner is 6 meters.
Hope that brings a smile to your face!
Let's assume the length of a blue banner is "B" and the length of a yellow banner is "Y".
According to the given information:
4B + 5Y = 49 (Equation 1)
2B + 1Y = 17 (Equation 2)
To find the length of a blue banner (B), we need to solve these two equations.
First, let's multiply Equation 2 by 2 to make the coefficients of B the same:
2(2B + 1Y) = 2(17)
4B + 2Y = 34 (Equation 3)
Now, we have two equations with the same coefficients for B:
4B + 5Y = 49 (Equation 1)
4B + 2Y = 34 (Equation 3)
Subtracting Equation 3 from Equation 1, we can eliminate B:
(4B + 5Y) - (4B + 2Y) = 49 - 34
4B - 4B + 5Y - 2Y = 15
3Y = 15
Y = 15 / 3
Y = 5
Now that we have the value of Y, we can substitute it back into Equation 2 to find the value of B:
2B + 1Y = 17
2B + 1(5) = 17
2B + 5 = 17
2B = 17 - 5
2B = 12
B = 12 / 2
B = 6
Therefore, the length of a blue banner is 6 meters.
To find the length of a blue banner, we can set up a system of equations based on the given information:
Let's represent the length of a blue banner as "x" and the length of a yellow banner as "y."
From the first piece of information, we know that the total length of 4 blue banners and 5 yellow banners is 49 m:
4x + 5y = 49 ------(Equation 1)
From the second piece of information, we know that the total length of 2 blue banners and 1 yellow banner is 17 m:
2x + y = 17 ------(Equation 2)
Now, we have a system of equations with two unknowns (x and y). We can solve this system to find the value of x (the length of a blue banner).
One common method to solve a system of equations is substitution. Let's solve Equation 2 for y and substitute it into Equation 1:
From Equation 2, we can express y in terms of x:
y = 17 - 2x
Substitute the value of y in Equation 1:
4x + 5(17 - 2x) = 49
Now, we can solve this equation to find the value of x.
Distribute 5 to (17 - 2x):
4x + 85 - 10x = 49
Combine like terms:
-6x + 85 = 49
Subtract 85 from both sides:
-6x = 49 - 85
-6x = -36
Divide both sides by -6:
x = -36 / -6
x = 6
Therefore, the length of a blue banner is 6 meters.
4 b + 5 y = 49
2 b + 1 y = 17
4 b + 5 y = 49
10b + 5 y = 85
-----------------subtract
-6 b = -36
b = 6