a large bow takes 5 feet of ribbon small bow takes 3 feet. 150 feet of ribbon is available to make 36 bows. how many bows small and large?

Question

write an equation, variables and solve.

Answer 1

5x + 3y = 150 (this equation represents the total feet in ribbon used)

x   +  y  = 36  (this equation represents the number of ribbons created)

 

Solve by substitution:

x=36-y

 

Substitute into first equation:

5(36-y) + 3y = 150

180 - 5y + 3y = 150

180 - 2y = 150

-180         -180   

       -2y=-30

            -2

 

y = 15

Substitute this into the second equation

x + 15 = 36

   - 15    -15

       x = 21

 

CHECK:

(x+y=36)

21+15=36

 

(5x + 3y = 150)

5(21) + 3(15) =

105+45=150