Stefan is helping his grandpa with a project. They need a board that is 1212
inches long. Stefan cut a piece that is too long. It has a percent error of 10%.
His grandpa says, "After you fix that board, make the next board twice as long as the length you cut the first time."
How long should Stefan cut the next board?
Enter your answer as a mixed number in simplest form in the box.
The percent error is given by the formula: Percent Error = ((|Measured Value - Actual Value|) / Actual Value) * 100%
In this case, the measured value is the length that Stefan cut, and the actual value is 1212 inches. The percent error is 10%.
Let's solve for the length that Stefan cut:
10 = ((|x - 1212|) / 1212) * 100
Divide both sides of the equation by 100:
0.1 = (|x - 1212|) / 1212
Multiply both sides of the equation by 1212:
0.1 * 1212 = |x - 1212|
121.2 = |x - 1212|
Since the percent error is positive, the length Stefan cut must be greater than 1212 inches:
x - 1212 = 121.2 or x - 1212 = -121.2
Solving the first equation for x:
x - 1212 = 121.2
x = 1212 + 121.2
x = 1333.2
Solving the second equation for x:
x - 1212 = -121.2
x = 1212 - 121.2
x = 1090.8
The length Stefan cut the first time could be either 1333.2 inches or 1090.8 inches.
According to Stefan's grandpa, he should cut the next board twice as long as the length he initially cut.
If the original length was 1333.2 inches, the next board should be 2 * 1333.2 = 2666.4 inches long.
If the original length was 1090.8 inches, the next board should be 2 * 1090.8 = 2181.6 inches long.
Thus, Stefan should cut the next board to be either 2666.4 inches or 2181.6 inches long, depending on the original length.