percentage

Question

68% of John's school are boys and there are 180 more boys than girls. How many students altogether?

Answer 1

B- Number of Boys      

G - Number of girls

 / Just choose a variable for unknown and convert the statements of problem to algebraic expression in terms of variable chosen and solve the problem. This way life becomes easy.

 

 { B - G = 180

  { 0.68( B + G ) = B

 

   0.32 B = 0.68G

 

   B/ G = 68/32 = 17/8

 

   B - 8/17 B = 180

 

   9/17 B = 180

 

   B = 340   G = 160

 

Answer 2

let x=# of girls

let x+180=# of boys

total # of students =x+x+180=2x+180

68%(2x+180)=x+180

0.68(2x+180)=x+180

1.36x+122.4=x+180

1.36x-x=180-122.4

0.36x=57.6

36x=5760

x=5760/36

x=160 girls

x+180=160+180=340 boys

160+340=500 students

Answer 3

A similar problem:

 

72% of John's school are boys and there are 150 more boys than girls. How many students altogether?

 

x := number of students altogether in John's school

 

b := number of boy students in John's school

 

g := number of girl students in John's school

 

x = b + g

 

b = x(72%) = x(72/100) = x(18/25)

 

b = g + 150

 

g = b – 150

 

x = b + b - 150 = 2b – 150

 

x = 2x(18/25) – 150 = (36/25) x – 150

 

Add –x+150 to both sides:

 

150 = (36/25 – 25/25) x = (11/25) x

 

Multiply both sides by 25/11:

 

x = 150(25/11) = 150(100/44)

 

x = 7500/22 = 3750/11 ≈ 340.90909090909091 ≈ 340 total students

Answer 4

Hi Yeshwanti;

68%=0.68

x=quantity of girls

x+180=quantity of boys

0.68(x+x+180)=x+180

0.68(2x+180)=x+180

1.36x+122.4=x+180

Subtract x from both sides...

1.36x-x+122.4=x-x+180

0.36x+122.4=180

Subtract 122.4 from both sides...

0.36x+122.4-122.4=180-122.4

0.36x=57.6

Divide both sides by 0.36...

(0.36x)/0.36=57.5/0.36

x=160

x+180=340

x+x+180=500

There are 500 students, 340 girls and 160 boys.

 

Let's check our work...

0.68(500)=340

340 is quantity of boys.

340-180=160

160 is quantity of girls.

340+160=500