David cuts a 6 metre long pole into three different pieces. The largest piece is 40 cm longer than the middle piece. The middle piece is 70 cm longer than shortest piece. What is the size of the largest piece?
x = shortest piece
x + x + 70 + x + 110 = 600
3x + 180 = 600
3x = 420
x = 140
Middle piece = 210
Longest piece = 250
Well, it appears that David really knows how to distribute his pole pieces! Let's solve this math mystery.
Let's call the size of the shortest piece "x". According to the information given, the middle piece is 70 cm longer than the shortest piece, so its size is "x + 70".
Now, here comes the big reveal! The largest piece is 40 cm longer than the middle piece, so its size is "(x + 70) + 40", or simply "x + 110".
But wait, there's more! We also know that the total length of all three pieces adds up to 6 meters, which is equivalent to 600 centimeters. So, we can set up an equation:
x + (x + 70) + (x + 110) = 600
Now, let's put on our detective hats and find the value of "x".
3x + 180 = 600
3x = 420
x = 140
Ah-ha! The shortest piece is 140 cm long. Now, let's unveil the size of the largest piece.
Largest piece size = x + 110
Largest piece size = 140 + 110
Largest piece size = 250 cm
Tada! The largest piece is a whopping 250 cm long. Watch out for that one; it's a real attention-grabber at parties!
Let's solve this step by step.
Let's assume the size of the shortest piece as x cm.
According to the given information, the middle piece is 70 cm longer than the shortest piece. So the size of the middle piece would be x + 70 cm.
The largest piece is 40 cm longer than the middle piece. So the size of the largest piece would be (x + 70) + 40 cm.
The sum of the three pieces should be equal to the original length of the pole, which is 6 meters or 600 cm.
So, we can write the equation: x + (x + 70) + ((x + 70) + 40) = 600
Now we can solve this equation to find the value of x and then find the size of the largest piece.
Combining like terms, we get: 3x + 180 = 600
Subtracting 180 from both sides, we get: 3x = 420
Dividing both sides by 3, we get: x = 140
So, the size of the largest piece is (x + 70) + 40 = 140 + 70 + 40 = 250 cm.
Therefore, the size of the largest piece is 250 cm.
To find the size of the largest piece, let's first assign variables for the lengths of the three pieces.
Let's say:
Shortest piece = x meters
Middle piece = y meters
Largest piece = z meters
We know the following relationships:
1. z = y + 0.4 meters (since 40 cm is equal to 0.4 meters)
2. y = x + 0.7 meters (since 70 cm is equal to 0.7 meters)
3. x + y + z = 6 meters (since the total length of the pole is 6 meters)
Now we have a system of three equations:
z = y + 0.4
y = x + 0.7
x + y + z = 6
To solve this system of equations, we can use substitution or elimination.
Using substitution, we substitute the value of y from equation 2 into equations 1 and 3:
z = (x + 0.7) + 0.4
x + (x + 0.7) + (x + 0.7 + 0.4) = 6
Simplifying equation 1:
z = x + 1.1
Simplifying equation 3:
3x + 2.1 = 6
3x = 6 - 2.1
3x = 3.9
x = 3.9 / 3
x = 1.3 meters
Now, substituting the value of x into equation 1 gives us:
z = 1.3 + 1.1
z = 2.4 meters
Therefore, the size of the largest piece is 2.4 meters.