The ratio of the lengths of two pieces of ribbon is 1:3. If 4 ft were cut from each piece, the sum of the new lengths would be 4 ft. How long would each piece be ?
length of original pieces : x and 3x
length of pieces after 4 ft cut off from each : x-4 and 3x-4
x-4 + 3x-4 = 4
4x = 12
x = 3
original pieces were 3 ft and 9 ft.
check:
new pieces: -1 and 5 , whose sum is 4 ?????
Even though the solution makes sense arithmetically, in reality this is a dumb question.
how can you cut off 4 ft from a ribbon only 3 ft long?
To solve this problem, we can set up an equation based on the given information. Let's call the lengths of the two pieces of ribbon x and y, where x and y are in feet.
According to the problem, the ratio of the lengths of the two pieces is 1:3. So, we can write:
x:y = 1:3
We can rewrite this ratio in terms of x and y:
x/y = 1/3
Now, we are told that if 4ft were cut from each piece, the sum of the new lengths would be 4ft. So, we can write:
(x - 4) + (y - 4) = 4
Now, we can solve this equation to find the values of x and y.
Let's simplify the equation:
x - 4 + y - 4 = 4
x + y - 8 = 4
Now, let's isolate the variable:
x + y = 4 + 8
x + y = 12
Since we have two variables (x and y) and only one equation, we cannot directly solve for their individual values. However, we can leverage the fact that the ratio of their lengths is 1:3.
If we express x and y in terms of a variable, say 3n, then we can substitute that into the equation:
x = 1n, y = 3n
Substituting these into the equation x + y = 12, we get:
1n + 3n = 12
4n = 12
n = 3
Now, we can find the values of x and y by substituting the value of n back into the expressions for x and y:
x = 1n = 1 * 3 = 3 ft
y = 3n = 3 * 3 = 9 ft
Therefore, the lengths of the two pieces of ribbon are 3 ft and 9 ft, respectively.