Problema Solution
Mary has 45 yards of ribbon and needs to cut it in 1/2 yard increments for decorations. How many decorations will she be able to make?
Answer provided by our tutors
Let 'x' represent the number of decorations that Mary is able to do from 45 yards of ribbon.
1 + 1/2 + ... + (x - 1)*(1/2) <= 45
(1/2)(0 + 1 + ... + (x - 1)) <= 45
(1/2)(x-1+1)(x-1)(1/2) <= 45
x(x-1)<= 180
If we graph y = x(x-1) - 180 we will see that for x < 14 the following inequality is valid: x(x-1)<= 180
So Mary can make 14 decorations at most.