In a class of 39 pupils, 1/4 of the girls wear spectacles and 2/3 of the boys wear spectacles. A total of 16 pupils in the class wear spectacles. How many girls do not wear spectacles?
Answer preferably in model method please.
Let's solve the problem step-by-step.
Step 1: Identify what is given in the problem.
- There are 39 pupils in the class.
- 1/4 of the girls wear spectacles.
- 2/3 of the boys wear spectacles.
- A total of 16 pupils in the class wear spectacles.
Step 2: Determine the number of boys and girls in the class.
- Let's assume there are B boys and G girls in the class.
- The total number of pupils in the class is 39: G + B = 39.
Step 3: Determine the number of girls who wear spectacles.
- 1/4 of the girls wear spectacles, so the number of girls who wear spectacles is (1/4)G.
Step 4: Determine the number of boys who wear spectacles.
- 2/3 of the boys wear spectacles, so the number of boys who wear spectacles is (2/3)B.
Step 5: Set up an equation using the given information.
- The total number of pupils who wear spectacles is 16: (1/4)G + (2/3)B = 16.
Step 6: Simplify the equation.
- Multiply both sides of the equation by the least common multiple (LCM) of 4 and 3, which is 12:
3G + 8B = 192.
Step 7: Use the equation to express one variable in terms of the other.
- We can solve the equation for G in terms of B:
3G = 192 - 8B
G = (192 - 8B)/3.
Step 8: Substitute the expression for G into the equation G + B = 39.
(192 - 8B)/3 + B = 39.
Step 9: Solve for B.
Multiply both sides of the equation by 3 to eliminate the fraction:
192 - 8B + 3B = 117.
-5B = 117 - 192
-5B = -75.
B = (-75)/(-5) = 15.
Step 10: Substitute the value of B back into the equation G = (192 - 8B)/3 to find G.
G = (192 - 8(15))/3
G = (192 - 120)/3
G = 72/3
G = 24.
Step 11: Calculate the number of girls who do not wear spectacles.
The number of girls who do not wear spectacles is the total number of girls minus the number of girls who wear spectacles: G - (1/4)G = 24 - (1/4)(24) = 24 - 6 = 18.
Therefore, there are 18 girls in the class who do not wear spectacles.
To solve this problem, we can use the model method. Let's break down the information given in the problem:
1. In the class, there are 39 pupils.
2. 1/4 of the girls wear spectacles.
3. 2/3 of the boys wear spectacles.
4. A total of 16 pupils wear spectacles.
Let's start by visualizing the model.
---------------
| Girls |
---------------
/ \
/ \
/ \
/ \
------- -------
| G1 | | B1 |
------- -------
| G2 | | B2 |
------- etc. -------
In the model, "G" represents girls, and "B" represents boys. The numbers indicate the number of students falling into each category.
Let's assume the number of girls is "x," and the number of boys is "y".
Based on the information given, we can write the equations:
(Number of girls / Total number of girls) * (Total number of pupils) = Girls who wear spectacles
(1/4) * x = Girls who wear spectacles
(Number of boys / Total number of boys) * (Total number of pupils) = Boys who wear spectacles
(2/3) * y = Boys who wear spectacles
Now, we can create another equation for the total number of pupils who wear spectacles:
Girls who wear spectacles + Boys who wear spectacles = Total number of pupils who wear spectacles
(1/4) * x + (2/3) * y = 16
Finally, we can create an equation to represent the total number of pupils in the class:
x + y = 39
Now we have a system of equations:
(1/4) * x + (2/3) * y = 16
x + y = 39
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using the elimination method:
Multiply the first equation by 12 to eliminate the fractions:
3x + 8y = 192
Now, subtract the second equation from the modified first equation:
(3x + 8y) - (x + y) = 192 - 39
2x + 7y = 153
Now we have a new equation:
2x + 7y = 153 (Equation 1)
We can solve Equation 1 simultaneously with the second equation:
x + y = 39 (Equation 2)
Multiply Equation 2 by 2:
2x + 2y = 78 (Equation 3)
Now subtract Equation 3 from Equation 1:
(2x + 7y) - (2x + 2y) = 153 - 78
5y = 75
Divide by 5:
y = 15
Substitute the value of y into Equation 2 to find x:
x + 15 = 39
x = 39 - 15
x = 24
Therefore, there are 24 girls and 15 boys in the class.
To find the number of girls who do not wear spectacles, we subtract the number of girls who wear spectacles from the total number of girls:
Girls who do not wear spectacles = Total number of girls - Girls who wear spectacles
Girls who do not wear spectacles = 24 - (1/4 * 24)
Girls who do not wear spectacles = 24 - 6
Girls who do not wear spectacles = 18
Therefore, there are 18 girls who do not wear spectacles in the class.