i have two piece of ribbon one is 17.5cm longer than the other and 1/3 of one ribbon is the same as 3/4 of the other what is the size of the smaller ribbon
(1/3) long , x = (3/4) short , y
x = y + 17.5
(y+17.5)/3 = 3 y/4
4 y + 70 = 9 y
5 y = 70
y = 14
L is longer ribbong length, S is shorter ribbon length
L-17.5=S
L/3=3S/4
L= 9S/4
9S/4 -17.5=S
S(9/4-4/4)=17.5
S= 4*17.5/5=14 inches
To find the length of the smaller ribbon, we can set up a system of equations based on the given information.
Let's assume the length of the smaller ribbon is x cm.
According to the problem statement, the larger ribbon is 17.5 cm longer than the smaller ribbon. Therefore, the length of the larger ribbon can be expressed as (x + 17.5) cm.
It is also given that 1/3 of one ribbon is the same as 3/4 of the other. We can write this as an equation:
(1/3) * x = (3/4) * (x + 17.5)
To solve for x, we can start by simplifying the equation:
x/3 = (3/4) * (x + 17.5)
Next, we can cross multiply:
4x = 3 * (x + 17.5)
After expanding:
4x = 3x + 52.5
Subtracting 3x from both sides:
x = 52.5
Thus, the size of the smaller ribbon is 52.5 cm.