1/5 of Chris's wire is equal to 1/4 of Sarah's. Daniel has 3 times as much wow as Sarah. In all, their wires measure 5 feet. How long is Chris's wire in feet.
Chris' wire ---- x
Daniel's wire --- y
Sarah's wire ---- z
x + y + z = 5
1/5 x = 1/4 z
x = (5/4)z
y = 3z
sub into x+y+z = 5
(5/4)z + 3z + z = 5
times 4
5z + 16z = 20
21z = 20
z = 20/21
y = 20/7
x = (5/4)(20/21) = 25/21
check: 20/21 + 20/7 + 25/21 = 5 ✔
Daniel's is 3 times as much as Sarah's : y = 3z
20/7 = 3(20/21) ✔
1/5 of Chris's wire is equal to 1/4 of Sarah's.
(1/5)(25/21) = (1/4)(20/21)
5/21 = 5/21 ✔
1 4/21
To find out how long Chris's wire is in feet, let's break down the given information step by step.
1. Let's assume the length of Chris's wire is "x" feet.
2. According to the given information, 1/5 of Chris's wire is equal to 1/4 of Sarah's wire.
This can be expressed as:
(1/5) * x = (1/4) * Sarah's Wire
Simplifying the equation, we get:
x/5 = Sarah's Wire/4
3. Next, we are told that Daniel has 3 times as much wire as Sarah. Let's represent the length of Sarah's wire as "y".
Daniel's wire = 3 * Sarah's Wire
= 3 * y
4. Finally, we are given that the total length of their wires is 5 feet. So, the equation becomes:
x + Sarah's Wire + Daniel's Wire = 5
Plugging in the values we have derived so far, we get:
x + y + 3y = 5
Simplifying the equation:
x + 4y = 5
Now, we have a system of two equations:
x/5 = y/4 ---- (Equation 1)
x + 4y = 5 ---- (Equation 2)
To solve this system of equations, we can use the substitution or elimination method. Since Equation 1 is already solved for "x", let's use substitution.
From Equation 1, we know that x = (5/4) * y.
Substituting this value of "x" in Equation 2:
(5/4) * y + 4y = 5
Simplifying the equation:
5y/4 + 4y = 5
Combining like terms:
5y + 16y = 20
21y = 20
Dividing by 21 on both sides:
y = 20/21
Therefore, the length of Sarah's wire (y) is 20/21 of a foot.
Now, let's substitute this value of "y" in Equation 1 to get the length of Chris's wire (x):
x/5 = (20/21)/4
Simplifying the equation:
x/5 = 20/84
Cross-multiplying:
84x = 100
Dividing by 84 on both sides:
x = 100/84
Simplifying the fraction:
x = 25/21
Therefore, the length of Chris's wire is 25/21 of a foot.