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
X=x
Y=(x+17.5)
1/3Y=3/4x
1/3(x+17.5)=3/4x
x+17.5=3/4x*3
x+17.5=9x/4
17.5=(9x/4)-x
17.5=(9x-4x)/4
17.5*4=5x
70=5x
14=x
So, shortest piece of ribbon is 14cm
that doesn't answer the question though does it ?
To find the size 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 given information, the larger ribbon is 17.5 cm longer than the smaller ribbon, so the length of the larger ribbon would be (x + 17.5) cm.
We also know that 1/3 of one ribbon is the same as 3/4 of the other. Mathematically, we can represent this as:
(1/3) * x = (3/4) * (x + 17.5)
Now, let's solve this equation to find the value of x, which represents the size of the smaller ribbon:
Multiply both sides of the equation by 12 to eliminate the fractions:
4x = 9(x + 17.5)
Expanding the equation:
4x = 9x + 157.5
Subtracting 9x from both sides:
4x - 9x = 157.5
-5x = 157.5
Dividing both sides by -5:
x = -157.5 / 5
x = -31.5
Therefore, the size of the smaller ribbon is -31.5 cm.
However, it is important to note that negative lengths don't make sense in this context. So, there might be an error in the problem statement or the given information. Double-check the problem or re-evaluate the information provided to get the correct result.
s = smaller , r = longer
s + 17.5 = r
r / 3 = 3 s / 4 ... 4 r = 9 s
solve the system