If the ratio of boys to girls is 3:2 and there are 25 students in a class, how do you make equal ratios to show how many students in the class are boys and how many are girls?

Question

Everly Taylor · Accepted Answer

The explanation is much longer than doing the mathematics.

The ratio of 15 boys to 10 girls is equivalent to the ratio of 3:2

Consider the starting point: We have 3 boys and 2 girls. This gives a total count of 5 So we need to see how many lots of 5 will fit into 25. 5 lots of 5 gives 25 So we have 5 lots of the ratio 3:2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Method 1")# 5 lots of 3:2 #-> 5xx ( 3:2) =(5xx3) : (5xx2) = 15:10# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Method 2")# Write the ratio in fractional form #color(magenta)("We can do this as long as we do not view and treat it like a fraction")# It does not matter in this case which we put on the top. I chose: #("boys")/("girls") -> 3/2# Multiply a value (or system) by 1 and you do not change the value. However, 1 comes in many forms. #color(green)(3/2color(red)(xx1) " "->" "3/2color(red)(xx5/5))# #" "=color(green)((3color(red)(xx5))/(2color(red)(xx5))# #" "=15/10 =("boys")/("girls") # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The ratio of 15 boys to 10 girls is equivalent to the ratio of 3:2 #15:10-=(15-:5):(10-:5)=3:2# where #-=# means equivalent to

Gabriel Agustin · Answer

undefined To find out how many students in the class are boys and how many are girls, we first need to split the total number of students (25) into parts according to the given ratio of boys to girls, which is 3:2.

1. First, find the total parts in the ratio by adding the parts together: $3 + 2 = 5$.
  
2. Then, divide the total number of students (25) by the total parts to find the value of one part: $25 \div 5 = 5$.

3. Multiply the value of one part by the number of parts for boys and girls respectively to find out how many boys and girls are in the class:
   
   For boys: $3 \times 5 = 15$ boys.
   
   For girls: $2 \times 5 = 10$ girls.

Therefore, in a class of 25 students with a ratio of boys to girls being 3:2, there are 15 boys and 10 girls.