the ratio of the number of boys to the number of girls in a class is 4:7. if there are 12 more girls than boys, find the total number of pupils in the class.
Wendy went to a bakery to buy cakes and doughnuts. She spent $14 altogether on 30 cakes and doughnuts. Each cake cost 40 cents and each doughnut cost 50 cents. How many cakes and doughnuts did she buy?
b = the number of boys
g = the number of girls
b / g = 4 / 7 Multiply both sides by 7
7 b / g = 4 Multiply both sides by g
7 b = 4 g Divide both sides by 4
7 b / 4 = g
g = 7 b / 4
g = 12 + b
7 b / 4 = 12 + b Subtract b to both sides
7 b / 4 - b = 12 + b - b
7 b / 4 - b = 12
7 b / 4 - 4 b / 4 = 12
3 b / 4 = 12 Multiply both sides by 4
3 b = 48 Divide both sides by 3
b = 48 / 3 = 16
g = b + 12 = 16 + 12 = 28
16 boys and 28 girls
The total number of pupils in the class = b + g = 16 + 28 = 44
Proof :
b / g = 16 / 28 = 4 * 4 / ( 4 * 7 ) = 4 / 7
g = b + 12
g = 16 + 12 = 28
To find the total number of pupils in the class, we need to determine the number of boys and girls separately.
Let's assume the number of boys as "4x" and the number of girls as "7x". This means that the ratio of boys to girls is 4:7.
According to the given information, there are 12 more girls than boys. So, we can set up the equation:
7x = 4x + 12
Now we'll solve the equation:
7x - 4x = 12
3x = 12
x = 12/3
x = 4
Now that we have the value of x, we can substitute it back into our initial assumptions:
Number of boys = 4x = 4 * 4 = 16
Number of girls = 7x = 7 * 4 = 28
The total number of pupils in the class is the sum of the number of boys and girls:
Total number of pupils = Number of boys + Number of girls
= 16 + 28
= 44
Therefore, there are a total of 44 pupils in the class.