A banquet hall has a perimeter of 3600 m. With is the width if the length is 5 times the width?

Answer:

$385

Step-by-step explanation:

Simplify the following:

(3 + 1/3)/(2 + 2/5)

Put 2 + 2/5 over the common denominator 5. 2 + 2/5 = (5×2)/5 + 2/5:

(3 + 1/3)/((5×2)/5 + 2/5)

5×2 = 10:

(3 + 1/3)/(10/5 + 2/5)

10/5 + 2/5 = (10 + 2)/5:

(3 + 1/3)/((10 + 2)/5)

10 + 2 = 12:

(3 + 1/3)/(12/5)

Put 3 + 1/3 over the common denominator 3. 3 + 1/3 = (3×3)/3 + 1/3:

((3×3)/3 + 1/3)/(12/5)

3×3 = 9:

(9/3 + 1/3)/(12/5)

9/3 + 1/3 = (9 + 1)/3:

((9 + 1)/3)/(12/5)

9 + 1 = 10:

(10/3)/(12/5)

Multiply the numerator by the reciprocal of the denominator, (10/3)/(12/5) = 10/3×5/12:

(10×5)/(3×12)

The gcd of 10 and 12 is 2, so (10×5)/(3×12) = ((2×5) 5)/(3 (2×6)) = 2/2×(5×5)/(3×6) = (5×5)/(3×6):

(5×5)/(3×6)

3×6 = 18:

(5×5)/18

5×5 = 25:

Answer: 25/18

1. We assume, that the number 312 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 312, so we can write it down as 100%=312.

4. We know, that x% equals 78 of the output value, so we can write it down as x%=78.

5. Now we have two simple equations:

1) 100%=312

2) x%=78

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=312/78

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 78 is what percent of 312

100%/x%=312/78

(100/x)*x=(312/78)*x - we multiply both sides of the equation by x

100=4*x - we divide both sides of the equation by (4) to get x

100/4=x

25=x

x=25

now we have:

78 is 25% of 312