A piece of lumber which is 55 inches long is cut into two parts such that 2 times the larger part will be 12 more than 5 times the smaller part. How long are each of the pieces of lumber?
Just make symbols out of the words, sentence by sentence.
two parts: x and 55-x
We can let x be the larger piece.
2x = 12 + 5(55-x)
2x = 12 + 275 - 5x
7x = 287
x = 41
so, the pieces are 41" and 14"
check:
82 = 12 + 70
16
To solve this problem, we need to set up an equation.
Let's assume that the length of the smaller part of the lumber is x inches. The length of the larger part will then be (55 - x) inches, as the two parts add up to a total length of 55 inches.
We are given that "2 times the larger part will be 12 more than 5 times the smaller part." In equation form, this can be written as:
2(55 - x) = 5x + 12
Now, we can solve for x by simplifying and solving the equation:
110 - 2x = 5x + 12
110 - 12 = 5x + 2x
98 = 7x
x = 98 / 7
x = 14
So, the smaller part of the lumber is 14 inches long.
To find the length of the larger part, we subtract the length of the smaller part from the total length:
55 - 14 = 41
Therefore, the larger part of the lumber is 41 inches long.
In summary, the smaller part is 14 inches long, and the larger part is 41 inches long.
6 = a/4 + 2
Is the answer 16? That's what i got