the ratio of the number of boys to the number of girls is 3 : 2. if each boy receives 2 pieces of paper and each girl receives 3 pieces of paper, how many children are there altogether if a total of 1992 pieces of paper are needed?
im not sure if this is right, but i got 797 children
since each group of 3 boys and 2 girls gets a total of 3*2+2*3=12 pieces of paper, there are
1992/12 = 166 groups of 5 children, or 830 in all
Too bad you didn't bother to show your work ...
To find the total number of children, we need to determine the number of boys and girls separately.
Let's assume the number of boys is 3x and the number of girls is 2x (since the ratio of boys to girls is 3:2).
Now, we can calculate the number of pieces of paper required for boys and girls:
For boys: 2 pieces of paper per boy
For girls: 3 pieces of paper per girl
The total number of pieces of paper for boys is 2 * (3x) = 6x.
The total number of pieces of paper for girls is 3 * (2x) = 6x.
Since the total number of pieces of paper is 1992, we can create the following equation:
6x + 6x = 1992
Simplifying the equation:
12x = 1992
x = 1992/12
x = 166
Now, we can find the total number of children by substituting the value of x back into the equations:
Number of boys = 3x = 3 * 166 = 498
Number of girls = 2x = 2 * 166 = 332
Therefore, the total number of children is 498 (boys) + 332 (girls) = 830.
To solve this problem, let's start by breaking down the information given:
Ratio of boys to girls: 3 : 2
This ratio indicates that for every 3 boys, there are 2 girls.
Next, we need to determine how many pieces of paper each child receives. The boys receive 2 pieces, and the girls receive 3 pieces.
Now let's proceed with the steps to find the total number of children:
Step 1: Determine the ratio multiplier.
To find the multiplier, we need to find the least common multiple (LCM) of the numbers 3 and 2. The LCM of 3 and 2 is 6.
So, the multiplier is 6.
Step 2: Calculate the total number of boys.
Since each boy receives 2 pieces of paper, we need to multiply the number of boys in the ratio (3) by the ratio's multiplier (6):
Total number of boys = 3 (boys) x 6 (multiplier) = 18 boys.
Step 3: Calculate the total number of girls.
Since each girl receives 3 pieces of paper, we need to multiply the number of girls in the ratio (2) by the ratio's multiplier (6):
Total number of girls = 2 (girls) x 6 (multiplier) = 12 girls.
Step 4: Calculate the total number of children.
To find the total number of children, we add the number of boys and girls together:
Total number of children = Total number of boys + Total number of girls
Total number of children = 18 (boys) + 12 (girls) = 30 children.
Therefore, there are 30 children altogether if a total of 1992 pieces of paper is needed.