How do I work this problem out

Question

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.

Answer 1

assume:

length of a blue banner B

length of yellow banner Y

this is a 2 equations in 2 unknowns (B and Y) problem

equation 1

4B + 5Y = 49

equation 2

2B + 1Y = 17

from equation 2, Y = 17 - 2B

substitute in equation 1, you get

4B + 5*(17-2B) = 49

4B + 85 -10B = 49

10B - 4B = 85 - 49

6B = 36

B ( the length of the blue banner) = 6 meters

and since Y = 17 - 2B, then Y = 17 - 2*6 = 17 - 12 = 5 meters

Y ( the length of the yellow banner) = 5 meters