David cuts a 6 metre long pole into three different pieces,The largest piece is 40cm longer than the middle piece and the middle piece is 70 cm longer than the shortest piece. What is the size of the largest piece ?

Question

David cuts a 6 metre long pole into three different pieces,The largest piece is 40cm longer than the middle piece and the middle piece is 70 cm longer than the shortest piece. What is the size of the largest piece ?

Answer 1

Shortest piece : x

middle piece : x+70
longest piece: x+70 + 40 = x+110

x + x+70 + x+110 = 600

solve for x, then evaluate x + 110

Answer 2

Let's assign variables to represent the lengths of the three pieces. Let's say the lengths of the shortest, middle, and largest pieces are x, y, and z respectively.

According to the given information:

1) The largest piece is 40 cm longer than the middle piece: z = y + 40

2) The middle piece is 70 cm longer than the shortest piece: y = x + 70

We also know that the total length of the pole is 6 meters, which is equal to 600 cm. So we have the equation:

x + y + z = 600

Now we can use these equations to solve for the variables.

Substituting the value of y from equation 2) into equation 1), we get:

z = (x + 70) + 40
z = x + 110

Substituting the values of x and z into equation 3), we have:

x + (x + 70) + (x + 110) = 600
3x + 180 = 600
3x = 600 - 180
3x = 420
x = 420/3
x = 140

Substituting the value of x into equation 2), we find:

y = 140 + 70
y = 210

Finally, substituting the values of x and y into equation 1), we get:

z = 210 + 40
z = 250

Therefore, the largest piece is 250 cm long.

Answer 3

To solve this problem, let's assign variables to the lengths of each piece. Let's call the length of the shortest piece x.

According to the problem, the middle piece is 70 cm longer than the shortest piece. So, the length of the middle piece can be represented as x + 70.

Similarly, the largest piece is 40 cm longer than the middle piece. So, the length of the largest piece can be represented as (x + 70) + 40.

Since the sum of the lengths of the three pieces should equal the length of the original 6-meter pole, we can set up an equation:

x + (x + 70) + ((x + 70) + 40) = 600 (we convert the 6 meters into centimeters)

Now, let's solve this equation:

3x + 180 = 600
3x = 600 - 180
3x = 420
x = 420 / 3
x = 140

So, the length of the shortest piece is 140 cm.

Now, let's find the length of the largest piece:

Largest Piece = (x + 70) + 40
= (140 + 70) + 40
= 210 + 40
= 250

Therefore, the size of the largest piece is 250 cm.