A 35 inch stick is cut up into two pieces. If the ratio of their lengths is 2:3, then how long is each piece?
Let the lengths of the two pieces be 2x and 3x, where x is a common factor.
We know that the total length is 35 inches, so we can write the equation:
2x + 3x = 35
Combining like terms:
5x = 35
Dividing both sides by 5:
x = 7
So one piece is 2x = 2(7) = 14 inches long.
The other piece is 3x = 3(7) = 21 inches long. Answer: \boxed{14, 21}.
Let's suppose that the length of the first piece is 2x inches and the length of the second piece is 3x inches.
According to the given information, the sum of the lengths of the two pieces is equal to the length of the stick:
2x + 3x = 35 inches
Combining like terms, we get:
5x = 35 inches
To solve for x, we divide both sides of the equation by 5:
x = 35 inches / 5
x = 7 inches
Now that we know the value of x, we can find the lengths of the two pieces:
Length of the first piece = 2x = 2 * 7 inches = 14 inches
Length of the second piece = 3x = 3 * 7 inches = 21 inches
So, each piece is 14 inches and 21 inches long, respectively.
To find the length of each piece, you'll need to use the given ratio and the total length of the stick. Here's how you can solve the problem step by step:
Step 1: Assign variables
Let's assign variables to the lengths of the two pieces. Let's call the length of the first piece 2x (since the ratio is 2:3) and the length of the second piece 3x.
Step 2: Set up the equation
The sum of the lengths of the two pieces should be equal to the total length of the stick, which is 35 inches. Therefore, you can set up the equation: 2x + 3x = 35.
Step 3: Combine like terms
Combine the like terms on the left side of the equation: 5x = 35.
Step 4: Solve for x
To isolate x, divide both sides of the equation by 5: x = 35/5.
Step 5: Calculate x
Simplify the right side of the equation: x = 7.
Step 6: Find the lengths of the pieces
Now that you have the value of x, substitute it back into the expressions for the two pieces:
Length of the first piece = 2x = 2 * 7 = 14 inches.
Length of the second piece = 3x = 3 * 7 = 21 inches.
So, the first piece is 14 inches long, and the second piece is 21 inches long.