I am sewing a skirt and i need a total of 390cm of different coloured ribbon. The white ribbon needs to be 40cm longer than the red ribbon while the blue ribbon needs to be 3 times as long as the red ribbon. the purple ribbon is half as long as the white ribbon. How long is each piece of ribbon
Total = 390 cm.
Red = X cm.
White = x+40 cm.
Blue = 3x cm.
Purple = (x+40)/2 = 0.5x+20.
x + (x+40) + 3x + (0.5x+20) = 390.
5.5x + 60 = 390,
X = 60 = Red.
Calculate the length of the other ribbons.
To solve this problem, let's assign variables to the lengths of each type of ribbon. Let's say the length of the red ribbon is 'x' cm.
1. We know that the white ribbon needs to be 40 cm longer than the red ribbon. So, the length of the white ribbon is (x + 40) cm.
2. The blue ribbon needs to be 3 times as long as the red ribbon. Therefore, the length of the blue ribbon is 3x cm.
3. The purple ribbon is half as long as the white ribbon. This means the length of the purple ribbon is (1/2)*(x + 40) cm.
To find the total length of all the ribbons, we can add up all the lengths:
Total length = length of red ribbon + length of white ribbon + length of blue ribbon + length of purple ribbon
Total length = x + (x + 40) + 3x + (1/2)*(x + 40)
Now, we can substitute the total length of 390 cm into the equation:
390 = x + (x + 40) + 3x + (1/2)*(x + 40)
Simplifying the equation:
390 = x + x + 40 + 3x + (1/2)*(x + 40)
Combining like terms:
390 = 5x + 80 + (1/2)*(x + 40)
Getting rid of the fraction by multiplying everything by 2:
780 = 10x + 160 + x + 40
Combine like terms:
780 = 11x + 200
Rearranging the equation:
11x = 780 - 200
11x = 580
Dividing both sides by 11:
x = 580/11
x ≈ 52.73
Now we can find the lengths of each ribbon:
Length of red ribbon: x = 52.73 cm
Length of white ribbon: x + 40 = 52.73 + 40 ≈ 92.73 cm
Length of blue ribbon: 3x = 3 * 52.73 ≈ 158.18 cm
Length of purple ribbon: (1/2)*(x + 40) = (1/2)*(52.73 + 40) ≈ 46.36 cm
So, the length of each piece of ribbon is approximately as follows:
Red ribbon: 52.73 cm
White ribbon: 92.73 cm
Blue ribbon: 158.18 cm
Purple ribbon: 46.36 cm