A survey conducted in a school showed that 65% of the pupils walked to school.the remaining number of pupils took buses to school the ratio of the number of pupils who took school buses to those who took public buses was 4:3.there were 360 more pupils who walked than those who took buses.how many pupils took public buses to school?
To find the number of pupils who took public buses to school, we need to go step by step through the given information.
Step 1: Calculate the total number of pupils who walked to school.
Let's assume the total number of pupils is x. Since 65% of the pupils walked to school, we can write an equation:
0.65x = Number of pupils who walked
Step 2: Calculate the total number of pupils who took buses to school.
The remaining percentage of pupils who took buses is 100% - 65% = 35%. We can write an equation:
0.35x = Number of pupils who took buses
Step 3: Calculate the ratio of the number of pupils who took school buses to public buses.
The ratio is given as 4:3. Let's assume the number of pupils who took school buses is 4y and the number of pupils who took public buses is 3y.
Step 4: Set up an equation to represent the remaining number of pupils who walked compared to those who took buses.
We know that the number of pupils who walked is 360 more than the number of pupils who took buses. So we can write an equation:
0.65x - 0.35x = 360
Now, let's solve these equations to find the answer.
Step 1: Simplify the equation for pupils who walked:
0.65x = Number of pupils who walked
Step 2: Simplify the equation for pupils who took buses:
0.35x = Number of pupils who took buses
Step 3: Set up a ratio equation:
4y/3y = 4/3
Step 4: Simplify the equation representing the remaining number of pupils who walked compared to those who took buses:
(0.65x - 0.35x) = 360
0.3x = 360
Step 5: Solve for x:
Multiply both sides of the equation by 10 to get rid of the decimal:
3x = 3600
Divide both sides of the equation by 3:
x = 1200
Step 6: Calculate the number of pupils who took public buses:
Substitute the value of x into the equation for pupils who took buses:
0.35x = 0.35 * 1200 = 420
Therefore, 420 pupils took public buses to school.
number who took the bus ---- x
"there were 360 more pupils who walked than those who took buses"
--> number who walked = x+360
(x+360) : x = 65% : 35% = 13 : 7
(x+360)/x = 13/7
13x = 7x + 2520
6x = 2520
x = 420
so 420 took the bus, and 780 walked
total number of students = 1200
(check: is .65 of 1200 = 780? YES)
last part:
school bus : public bus = 4 : 3 = 4k : 3k
7k = 420
k = 60
then 4k = 240, and 3k = 180
The number who took the public bus is 3k or
180.
check that one:
school : public = 180 : 240 = 3 : 4