4
5
of Chris's wire is equal to all of Daniel's. Daniel has
1
3
as much wire as Sarah. In all, their wires measure 8 feet. How long is Daniel's wire in feet
learn to type fractions
4/5 c = d, so c = 5/4 d
d = 1/3 s, so s = 3d
c+d+s = 8
substituting, you now have
5/4 d + d + 3d = 8
Let's break down the information given step by step to find out the length of Daniel's wire.
1. Let's assume the length of Sarah's wire is x feet.
2. According to the statement, Daniel has 3 times as much wire as Sarah, so Daniel's wire length is 3x feet.
3. The sum of Chris's and Daniel's wire length is 8 feet. Since Chris's wire is equal to all of Daniel's, we can write the equation: x + 3x = 8.
4. Simplifying the equation, we have 4x = 8.
5. Dividing both sides of the equation by 4, we find x = 2.
6. Now that we know the length of Sarah's wire is 2 feet, we can calculate the length of Daniel's wire: 3x = 3 * 2 = 6 feet.
Therefore, Daniel's wire is 6 feet long.
To find out how long Daniel's wire is, let's break down the information given and solve step by step.
Let's assign variables to represent each person's wire length:
- Let's represent Chris's wire length as 'C.'
- Let's represent Daniel's wire length as 'D.'
- Let's represent Sarah's wire length as 'S.'
From the first sentence, it states that 4/5 of Chris's wire is equal to all of Daniel's wire. So we can write the equation:
D = (4/5) * C
The second sentence tells us that Daniel has 1/3 as much wire as Sarah. So we can write the equation:
D = (1/3) * S
Finally, the last sentence states that the total length of their wires is 8 feet:
C + D + S = 8
Now we have a system of three equations:
D = (4/5) * C (Equation 1)
D = (1/3) * S (Equation 2)
C + D + S = 8 (Equation 3)
To find Daniel's wire length (D), we need to solve this system of equations.
First, let's solve for C in Equation 1:
C = (5/4) * D
Now, substitute this value of C in Equation 3:
(5/4) * D + D + S = 8
(9/4) * D + S = 8
Next, let's solve for S in Equation 2:
S = 3D
Now, substitute this value of S in Equation 3:
(9/4) * D + 3D = 8
(21/4) * D = 8
To solve for D, multiply both sides by 4/21:
D = (8 * 4) / 21
D = 32 / 21
D ≈ 1.5238 feet
Therefore, Daniel's wire is approximately 1.5238 feet long.