David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece is 3 ft more than 2 times the length of the shorter piece.
David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece is 3 ft more than 2 times the length of the shorter piece.
How long will each piece of hose be?
What does x represent the smaller or bigger piece?
NM its 12 and 15 for anybody who need the answer:3
x + 2x + 3 = 27
3x = 24
x = 8
To solve this problem, we can set up an equation based on the information given. Let's let x represent the length of the shorter piece.
According to the problem, the longer piece is 3 ft more than 2 times the length of the shorter piece. So, the length of the longer piece would be 2x + 3.
Now, we know that the total length of the hose is 27 ft. Therefore, we can add the lengths of the shorter and longer pieces to get:
x + (2x + 3) = 27
To solve the equation, we can combine like terms:
3x + 3 = 27
Subtracting 3 from both sides gives:
3x = 24
Now we can solve for x by dividing both sides by 3:
x = 8
So the shorter piece of the hose is 8 ft.
To find the longer piece, we can substitute the value of x back into our expression for the longer piece:
2x + 3 = 2(8) + 3 = 19
Therefore, the longer piece is 19 ft.