A plumber would like to cut a pipe 60 cm long into two piece. One piece is 10 cm longer than the other. Find the length of the two piece
a = first piece
b = second piece
One piece is 10 cm longer than the other mean:
b = a + 10
a + b = 60
a + a + 10 = 60
2 a + 10 = 60 Subtract 10 to both sides
2 a + 10 - 10 = 60 - 10
2 a = 50 Divide both sides by 2
a = 50 / 2 = 25 cm
b = a + 10
b = 25 + 10 = 35 cm
Well, it sounds like the plumber is in a bit of a pickle! To figure out the lengths of the two pieces, let's give them some names. We'll call the shorter piece "X" and the longer piece "Y".
Now, we know that the longer piece is 10 cm longer than the shorter piece. So, we can write an equation: Y = X + 10.
We also know that the total length of the pipe is 60 cm. So, the equation for that is: X + Y = 60.
Now, let's use our fabulous math skills to solve this problem with a touch of humor. We'll substitute the value of Y from the first equation into the second equation:
X + (X + 10) = 60.
Combining like terms, we get:
2X + 10 = 60.
To isolate X, we subtract 10 from both sides:
2X = 50.
Finally, we divide both sides by 2:
X = 25.
So, the shorter piece is 25 cm long. But wait, we haven't found the length of the longer piece yet! To do that, we can substitute the value of X into the equation Y = X + 10:
Y = 25 + 10.
Giving us:
Y = 35.
So, the longer piece is 35 cm long. Ta-da! We've solved the puzzle. The shorter piece measures 25 cm, and the longer piece measures 35 cm. Happy plumbing!
Let's call the length of the shorter piece x cm.
According to the problem, the longer piece is 10 cm longer than the shorter piece. Therefore, the length of the longer piece can be expressed as (x + 10) cm.
The sum of the lengths of the two pieces should be equal to the original length of the pipe, which is 60 cm. So we can write the following equation:
x + (x + 10) = 60
Now, let's solve for x:
2x + 10 = 60
Subtracting 10 from both sides:
2x = 50
Dividing both sides by 2:
x = 25
Therefore, the length of the shorter piece is 25 cm, and the length of the longer piece is 25 + 10 = 35 cm.
To find the length of the two pieces, let's assign variables to represent their lengths. Let's say the length of one piece is x cm.
According to the problem, the other piece is 10 cm longer than the first piece. So, the length of the other piece can be represented as (x + 10) cm.
Now, we know that the total length of the pipe is 60 cm. Therefore, we can write the equation:
x + (x + 10) = 60
Now, we can simplify and solve this equation:
2x + 10 = 60
2x = 60 - 10
2x = 50
x = 50/2
x = 25
So, the length of one piece is 25 cm, and the length of the other piece (which is 10 cm longer) is 25 + 10 = 35 cm.
Therefore, the two pieces are 25 cm and 35 cm in length respectively.