Question

A wood piece 100 cm long cut into two pieces so that the longer piece is 10 cm long than twice the length of shorter piece. What is the length of longer piece?

Answer 1

Answer: The short side is 30 cm and the long side is 70cm

Step-by-step explanation: We can define L as the lenght of the long side and S as the length of the short side:

The equations that we have are:

S + L = 100cm

L = 10cm + 2*S

Now we have two equations and two variables.

We can replace the second equation into the first one, and get:

S + 10cm + 2*S = 100cm

And we solve it for S

3*S + 10cm = 100cm

3*S = 90cm

S = 90cm/3 = 30cm

So the short side is 30cm, and the long side must be 100cm - 30cm = 70cm

Answer 2

For this case we propose a system of equations:

x: Let the variable representing the length of the longer piece

y: Let the variable representing the length of the shorter piece

According to the statement data we have:

`x + y = 100\\x = 10 + 2y`

Substituting the second equation into the first we have:

`10 + 2y + y = 100\\10 + 3y = 100\\3y = 100-10\\3y = 90\\y = \frac {90} {3}\\y = 30`

Thus, the shorter piece is 30 cm.

`x = 10 + 2y\\x = 10 + 2 (30)\\x = 10 + 60\\x = 70`

Thus, the longer piece is 70 cm.

Answer:

The longer piece is 70 centimeters.