use guess and check to solve the following problem. Write your solution as a sentence. A cable 84 meters long is cut into two pieces so that one piece is 18 meters longer than the other. Find the length of each piece of cable.
To solve the problem using guess and check, we can start by making some reasonable guesses for the length of one piece of the cable.
Let's assume that the length of the shorter piece is 30 meters. Since the longer piece is 18 meters longer than the shorter piece, it would be 30 + 18 = 48 meters.
Now let's check if the sum of these two pieces is equal to the total length of the cable, which is 84 meters. 30 + 48 = 78, which is less than 84.
Since the sum is less than 84, we need to increase the length of each piece. Let's try adding 1 meter to both guesses.
The new guesses are:
Shorter piece: 30 + 1 = 31 meters
Longer piece: 48 + 1 = 49 meters
Now, let's check if the new sum is equal to 84. 31 + 49 = 80, which is still less than 84.
We can continue increasing the length of each piece by 1 meter and checking if the sum equals 84.
By repeating this process, we will eventually find the solution. In this case, the correct lengths of the two pieces of cable are:
Shorter piece: 42 meters
Longer piece: 42 + 18 = 60 meters.
Thus, the length of each piece of the cable is 42 meters and 60 meters, respectively.