Let's figure out how much of the ribbon has been cut.
Let x = the original length of the ribbon
Aleena initially cuts 3/8 of the ribbon, or a length of (3/8)x. How much is left? 1 - (3/8)x = (5/8)x.
On the next day, she cuts 4/5 of the remaining ribbon. That is (4/5) * (5/8)x = (20/40)x = (1/2)x
How much of the ribbon has she now cut away?
(3/8)x + (1/2)x = (3/8)x + (4/8)x = (7/8)x
That means that 1 - (7/8)x = (1/8)x remains, and that is a length of 6.5 m.
We now need to determine the following:
1/8 of what number is 6.5?
Let y = the unknown number.
(1/8)y = 6.5
Multiply both sides of the equation by 8 to clear the fraction.
y = 52 m
