Question

Oliver interviewed 30% of the 9th grade class and 70% of the 10th grade class at his school. Jenny interviewed 75% of the 9th grade class and 25% of the 10th grade class at the same school. Oliver interviewed a total of 176 students and Jenny interviewed 140 students.

How many more 10th graders than 9th graders were interviewed?
A
36

B
80

C
120

D
200

Answer 1

A . 36

Explanation:

We are given a total of 176 interviewed by Oliver and a total of 140 interviewed by Jenny. To find how many more 10th graders than 9th graders were interviewed, subtract the totals given

176 - 140 = 36

This is how we came to the answer:

We are given 70% of the 10th-grade and 30% of the 9th-grade with a total of 176 for Oliver.

While we're given 75% of the 9th-grade class and 25% of the 10th-grade with a total of 140 interviewed by Jenny

Oliver's Interviewees

• 10-graders

Firstly, let's find what the number of 9th-graders was interviewed by Oliver; find the percentage of the 9th-graders by the total;

70% of 176 =

`(70)/(100) * (176)/(1)`

Cross multiply

123.2 were 10-graders interviewed by Oliver

• 9th-graders

Now, to find the number of 9th-graders was interviewed by Oliver; find the percentage of the 9th-graders by the total;

30% of 176 =

`(30)/(100) * (176)/(1)`

Cross multiply

52.8 were 9th-graders interviewed by Oliver

Jenny's Interviewees

• 9th-graders

Firstly, let's find what the number of 9th-graders was interviewed by Jenney; find the percentage of the 9th-graders by the total;

75% of 140 =

`(75)/(100) * (140)/(1)`

Cross multiply

105 students were 9th-graders interviewed by Jenney.

• 10th-graders

Now, to find the number of 10th-graders was interviewed by Jenney; find the percentage of the 10th-graders by the total;

25% of 140 =

`(25)/(100) * (140)/(1)`

Cross multiply

35 students were 10th-graders interviewed by Jenney.

Total calculation

Use the results and sum them up by 9th-grade plus 9th-grade and 10th-grade plus 10-grade. Then subtract the amount gotten from 9th-grade away from the amount gotten from 10th-grade;

Oliver's 9th-grade = 52.8

Jenny's 9th-grade = 105

105 + 52.8 = 157.8

Oliver's 10th-grade = 123.2

Jenny's 10th-grade = 35

123.2 + 35 = 158.2

Total calculation: 158. 2 - 157.8 = 0.4

Therefore, there are 36 more 10th than 9th.

Extra Info:

Oliver's Interviewees Percentage

Since we are given 30% of the 9th-grade class and 70% of the 10th-grade class, first, let's add the percentages. To do so, set it up as a fraction;

30% =
`(30)/(100)` while, 70% =
`(70)/(100)`

Now solve it;

`(30)/(100) + (70)/(100)`

Simplify; cancel bottom zero's;

`(30)/(1) + (70)/(1)`

Add the remaining numerators;

30 + 70 = 100

Which is 100%

Jenny's Interviewees Percentage

Since we're given 75% of the 9th-grade class and 25% of the 10th-grade, it will end up the same answer. I'll show you how; first, let's add the percentages. To do so, set it up as a fraction;

25% =
`(25)/(100)` and, 75% =
`(75)/(100)`

Now solve it;

`(25)/(100) + (75)/(100)`

Simplify; cancel bottom zero's

`(25)/(1) + (75)/(1)`

Add the remaining numerators;

25 + 75 = 100

Meaning 100%