Two problems?

Question

I have two questions....

1. Find two consecutive even numbers such that the sum of one-sixth the larger number and one-fourth the smaller number is two less than one-half the smaller humber.

The numbers are __ and __.

2. One-fifth the perimeter of a building is 50 feet. The length of the building is 30 feet longer than the width. Find the dimensions of the building.

The dimensions of the building are ___ ft. wide by ___ ft. long.

Thanks!

Answer 1

1.Let the numbers be x and x+2
By the problem,
1/6(x+2)+1/4(x)=x/2 -2
=> 2(x+2)+3x=6x-24[multiplying all trms by 12]
=>2x+4+3x=6x-24
=>2x+3x-6x= -24-4
=>-x= -28
x=28
Therefore the numbers are 28 and 28+2 or 30
2.Let the width be w ft.,then the length of the building is w+30 ft
Hence perimeter
=2(w+w+30)
=2(2w+30)
=4w+60
but it is given that 1/5th of the perimetr is 50 ft or the perimetr is 250 ft
therefore,
4w+60=250
=>4w=250-60=190
w=190/4=47.5 ft
Hence the width of the building is 47.5 ft and its length is 47.5+30 or 77.5 ft.

Answer 2

1

Answer 3

Answer 1:
Let the numbers be x and x + 2

[(x + 2)/6] + (x/4) = (x/2) - 2
[2(x + 2) + 3x]/12 = (x - 4)/2
(5x + 4)/12 = (x - 4)/2
2(5x + 4) = 12(x - 4)
10x + 8 = 12x - 48
10x - 12x = -48 - 8
-2x = -56
2x = 56
x = 28
x + 2 = 30

The numbers are 28 and 30

Answer 2:
Perimeter/5 = 50
Perimeter = 250 feet.

Let the width be x and the length be x + 30

2(x + x + 30) = 250
2(2x + 30) = 250
4x + 60 = 250
4x = 190
x = 190/4
x = 47.5 feet
x + 30 = 77.5 feet

he dimensions of the building are 47.5 ft. wide by 77.5 ft. long.

Answer 4

1.

x = smaller even number
x+2 = bigger even number

(x+2)/6 + x/4 = x/2 -2

The numbers are 16 and 18

2.

(2x + 2(x+30))/5 = 50

The dimensions of the building are 60 ft. wide by 90 ft. long.

Answer 5

1. The president taking away from his duties of governing the country and spending his energies instead on campaigning for reelection. His first term decisions are made with an eye toward positioning himself for an upcoming election, instead of what is best for the country. 2. There is nothing to stop a company from charging the federal government more than the original terms agreed upon in the bid. Cost overruns are an excepted part of government spending. Interestingly, the Confederate Constitution addressed both of these problems.

Answer 6

2. 110 ft. wide by 140 ft. long

Answer 7

for number 2:

the width is 47.5 and the lenght is 77.5