Half of Sarah's wire is equal to 2/5 of Daniels. Chris has 3 times as much as Sarah. In all, their wire measures 6 ft. How long is Sarah's wire in feet?
1/2 S=2/5 D
S=4/5 D
C=3S=6/5D
S+C+D=6
6/5 D + 4/5 D + D=6
3D=6
D=2
S= 4/5 D=8/5
C=6/5 D=12/5
check, add them up to see if it is aix feet.
Dan ---- x
Sarah ---(2/5)x
Chris --- (6/5)x
x + 2x/5 + 6x/5 = 6
times 5
5x + 2x + 6x = 30
13x = 30
x = 30/13 ft
Sarah --- (2/5)(30/13) = 12/13
(chris has (6/5)(30/13)= 36/13
check: 30/13 +12/13 + 36/13 = 78/13 = 6
my answer is correct
diagram needed
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To find out the length of Sarah's wire, let's break down the information given step by step:
1. Let's assume Sarah's wire is "x" feet long.
2. Half of Sarah's wire is equal to 2/5 of Daniel's wire, so we can set up an equation: (1/2)x = (2/5)y, where "y" is the length of Daniel's wire.
3. Chris has 3 times as much wire as Sarah, so Chris's wire is 3x feet long.
4. The total length of their wire is given as 6 feet, so we can set up another equation: x + y + 3x = 6.
Now we can solve these equations to find the length of Sarah's wire.
From equation 4, we have x + y + 3x = 6.
Combining like terms, we get 4x + y = 6. Equation (5)
From equation 2, we have (1/2)x = (2/5)y.
Multiply both sides by 2 to get rid of the fraction: x = (4/5)y. Equation (6)
Substitute the value of x from Equation (6) into Equation (5):
4(4/5)y + y = 6.
Multiplying, we get (16/5)y + (5/5)y = 6.
Combining like terms, we get (21/5)y = 6.
Multiply both sides by 5/21 to isolate y: y = (6 * 5) / 21.
Simplifying the right side, we get y = 30 / 21.
Dividing 30 by 21, we get y = 1.43 (rounded to two decimal places).
Now, let's substitute the value of y back into Equation (6) to find the length of Sarah's wire:
x = (4/5)y = (4/5) * 1.43.
Multiplying, we get x = 1.144 (rounded to three decimal places).
Therefore, Sarah's wire is approximately 1.144 feet long.