A ribbon measuring (v+4) feet in length was cut into two pieces in the ratio 3:7 What was the length of the longer piece
Let n be the common factor between the two pieces. Then, the length of each piece is given by 3n and 7n, respectively. The length of the longer piece would be 7n/v+4 So:
3n+7n=v+4
3n+7n/v+4=1
3n/v+4 +7n/v+4=1
7n/v+4=1-3n/v+4
You started well.
Ok, up to 3n+7n = v+4 , you have like terms in n
10n = v+4
n = (v+4)/10
so the longer piece is 7n or
7(v+4)/10
or
(7/10)(v+4)
To find the length of the longer piece, we first need to determine the total length of the ribbon.
The given information states that the ribbon measuring (v+4) feet in length was cut into two pieces in the ratio 3:7. This means that the total length of the ribbon is divided into 3 + 7 = 10 equal parts.
To calculate the length of each part, we divide the total length of the ribbon by the number of parts:
Length of each part = (v+4) feet / 10
Next, we need to determine the length of the longer piece, which is represented by 7 parts out of the total of 10 parts:
Length of longer piece = Length of each part * Number of parts (7 out of 10)
By substituting the expression for the length of each part, we get:
Length of longer piece = ((v+4) feet / 10) * (7 out of 10)
Thus, the length of the longer piece is ((v+4) feet / 10) * 7.