There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys is 5:3.There are 178 more Chinese boys than Malay boys.How many girls are there in the hall?
first step: express the clues algebraically:
boys/girls = 2/3
cboys/mboys = 5/3
cboys = mboys+178
Now, we want to find the number of girls. Just for ease of algebra, let's change the above to
b/g = 2/3
c/m = 5/3
c = m+178
3c = 5m
3(m+178) = 5m
2m = 534
m = 267
So, there are 267 Malay boys and 445 Chinese boys. That means b=712.
Now, we know that 3b=2g, so
g = 3/2 * 712 = 1068
So, there are 1068 girls in the hall.
Step 1: Assign variables
Let's assign variables to represent the number of Chinese boys, Malay boys, Chinese girls, and Malay girls.
Let:
Chinese boys = 5x
Malay boys = 3x
Chinese girls = 2y
Malay girls = 3y
Step 2: Translate the given information into equations
The ratio of the number of boys to the number of girls is 2:3. This can be written as:
(5x + 3x) : (2y + 3y) = 2 : 3
Simplifying the equation, we get:
8x : 5y = 2 : 3
Since there are 178 more Chinese boys than Malay boys, we can say:
5x - 3x = 178
Simplifying, we have:
2x = 178
Step 3: Solve for x
To solve for x, divide both sides of the equation by 2:
x = 178 / 2
x = 89
Step 4: Find the number of girls in the hall
Now that we know the value of x, we can substitute it back into the equation to find the number of girls. Let's find the value of y:
Chinese girls = 2y = 2 * y
Malay girls = 3y = 3 * y
Since Chinese boys = 5x, and Malay boys = 3x, we have:
5x = 5 * 89 = 445 (Chinese boys)
3x = 3 * 89 = 267 (Malay boys)
From the given information, we know that there are 178 more Chinese boys than Malay boys. Therefore:
Chinese boys - Malay boys = 445 - 267 = 178
Now, let's substitute the values into the equation and solve for y:
(5x + 3x) : (2y + 3y) = 2 : 3
(445 + 267) : (2y + 3y) = 2 : 3
712 : 5y = 2 : 3
To find the value of y, we'll cross-multiply:
3 * 712 = 2 * 5y
2136 = 10y
y = 2136 / 10
y = 213.6
Since the number of girls must be a whole number, we can conclude that there is an error in the given information or question. Please recheck the information or context related to the problem.
To find the number of girls in the hall, we need to follow a step-by-step approach.
Let's assume the number of Chinese boys is 5x, the number of Malay boys is 3x, the number of Chinese girls is 2y, and the number of Malay girls is 3y.
According to the given information, the ratio of the number of boys to the number of girls is 2:3. Therefore, we can write the equation:
(5x + 3x) : (2y + 3y) = 2 : 3
Simplifying the equation, we get:
8x : 5y = 2 : 3
To make the equation more manageable, we can multiply both sides by a factor of 15:
120x : 75y = 30 : 45
Simplifying again, we get:
8x : 5y = 2 : 3
24x : 15y = 6 : 9
Since the ratio of Chinese boys to Malay boys is 5:3, we can write the equation:
5x : 3x = 5 : 3
Simplifying this equation, we have:
15x = 9x + 178
Solving for x, we subtract 9x from both sides:
6x = 178
Dividing both sides by 6, we find:
x = 178 / 6 = 29.67
Since we can't have fractions of students, we round x to the nearest whole number:
x ≈ 30
Now, we can find the number of Chinese boys by substituting x = 30 into the equation:
5x = 5 * 30 = 150
Similarly, we can find the number of Malay boys:
3x = 3 * 30 = 90
Now that we have the number of Chinese boys and Malay boys, we can find the number of Chinese girls and Malay girls:
Number of Chinese girls = 2y = 2 * 30 = 60
Number of Malay girls = 3y = 3 * 30 = 90
Finally, to find the total number of girls in the hall, we add the number of Chinese girls and Malay girls:
Total number of girls = 60 + 90 = 150
Therefore, there are 150 girls in the hall.