Answer:
length of each ribbon was 50 inches.
Step-by-step explanation:
We have been given that she cuts 9 pieces of the same length, L, from the first ribbon and finds that 5 inches are left over.
It means she had a total of 9L length of ribbon and if we add 5 to this, it should be equal to the original length of the ribbon when she bought.
If x be the length of the each ribbon when she bought them. It means if we add 5 to 9L then it should be equal to x.
[tex]9L+5=x\\\\9L=x-5\\\\L=\frac{1}{9}(x-5)...(1)[/tex]
On the same way, we have the second equation as
[tex]2L+40=x[/tex]
Plugging the value of L from equation 1, we get
[tex]2\cdot(\frac{1}{9}(x-5))+40=x\\\\\frac{2}{9}x-\frac{10}{9}+40=x=x\\\\\frac{2}{9}x+\frac{350}{9}=x\\\\\frac{350}{9}=x-\frac{2}{9}x\\\\\frac{350}{9}=\frac{7x}{9}\\\\x=50[/tex]
Hence, length of each ribbon was 50 inches.
