Answer: The first option
Explanation:
What we know:
- 1 mile is equal to 5,280 feet
- The length of the fence is 1/4 mile
- The width of the fence is 1/8 mile
How to solve:
By finding the perimeter of the fence in feet, we can check that value against the 4 proportion options listed in the problem. Whichever is true will be the correct answer.
Process:
Perimeter - in feet
Where P is perimeter in miles, x is perimeter in feet, w is width in miles, and L is length in miles.
Set up equation P = 2w + 2L
Substitute P = 2(1/8) + 2(1/4)
Simplify P = 2/8 + 2/4
Common denominator P = 1/4 + 2/4
Simplify P = 3/4 mi.
Translate x = (3/4)*5280
Simplify x = 3960 ft.
For the following: Where m represents the mile unit, f represents the foot unit, and x represents the number of feet of fencing.
First option
Set up equation (3/4)m/x = m/5280f
Equal variables 16[(3/4)m/x) = 12[m/5280f]
Simplify 12m/16x = 12m/63360f
Remove miles 16x = 63360f
Isolate x variable /16 /16
Solution x = 3960 ft.
Second Option
Set up equation (3/8)m/x = m/5280f
Equal variables 64[(3/8)m/x] = 24[m/5280f]
Simplify 24m/64x = 24m/126720f
Remove miles 64x = 126720f
Isolate x variable /64 /64
Solution x = 1980 ft.
Third Option
Set up equation x/(3/4)f = m/5280f
Equal variables 7040[x/(3/4)f] = m/5280f
Simplify 7040x/5280f = m/5280f
Remove feet 7040x = m
Translate 7040x = 5280f
Isolate x variable /7040 /7040
Solution x = (3/4)f
Fourth Option
Set up equation x/(3/8)f = m/5280f
Equal variables 14080[x/(3/8)f] = m/5280f
Simplify 14080x/5280f = m/5280f
Remove feet 14080x = m
Translate 14080x = 5280f
Isolate x variable /14080 /14080
Solution x = 3/8f
Answer: The first proportion
Check:
If the perimeter of the fence, in feet, is the first option, then when
x = 3960, the number of miles and feet should be equal. Let's test this.
(3/4)m/x = 1
(3/4)m/3960f = 1
(3/4)(5280f)/3960f = 1
3960f/3960f = 1
1 = 1
Therefore, option 1 is correct.
