Word problem

Question

there are 3:5 ratio of boys to girls. If there are 300 more girls how many boys are there 

Answer 1

For every 8 persons

3/8 are boys (b)

5/8 are girls (g)

 

b = (3/8)(b + g)   the # of boys is 3/8 of the total kids

 

g = b + 300        their are 300 more girls than boys

 

replace g with b+300 in first equation

 

b = (3/8)(b + b + 300)

b = (3/8)(2b+300)         multiply both sides by 8

8b = 3(2b + 300)          distribute the 3 through

8b = 6b + 900              subtract 6b from both sides

2b = 900                      divide both sides by b

b = 450

 

g = b + 300 = 750

 

There are 450 boys and 750 girls

Answer 2

The question asks, "...how many boys are there," so, assign a variable to that value: Let b=number of boys

 

"there are 3:5 ratio of boys to girls"     means

     The boys to girls ratio is 3/5      [a ratio may be written as a fraction]

 

"300 more girls"     means

      3/5   =  b / (b+300)

 

Now, cross-multiply to get:

     5b = 3(b+300)

     5b = 3b + 900

     2b = 900

     b = 450

 

There are 450 boys  

  {note: you could calculate the number of girls simply to check your answer]