If a piece of wood is 5 cm longer than a second piece, and 3/4 of the second piece is equal to 3/5 of the first, what is the length of the second piece? Explain your workings
I think I answered this before.
If second piece = x, then first = x+5.
3/4x = 3/5(x+5)
Solve for x.
To solve this problem, let's assume the length of the second piece of wood is x cm.
According to the problem, the first piece of wood is 5 cm longer than the second piece. So, the length of the first piece would be (x + 5) cm.
It is also given that 3/4 of the second piece is equal to 3/5 of the first piece. Mathematically, we can represent this as:
(3/4) * x = (3/5) * (x + 5)
Now, let's solve this equation step by step:
Step 1: Simplify the equation by multiplying both sides by the least common denominator (LCD) of 4 and 5, which is 20:
20 * (3/4) * x = 20 * (3/5) * (x + 5)
Step 2: Simplify further:
15x = 12(x + 5)
Step 3: Expand the equation by multiplying:
15x = 12x + 60
Step 4: Simplify and isolate the variable:
15x - 12x = 60
3x = 60
Step 5: Solve for x by dividing both sides by 3:
x = 20
Hence, the length of the second piece of wood is 20 cm.