We are given with two equations 2x − 3y = −1 and 11x − 9y = −13. The problem says that when the first equation is multiplied by -3 which results to -6x + 9y = 3, the sum of the resulting equation and the second one is equal to 5x = -10. We verify this: -6x + 11x = 5x while -9 y and 9 y cancels out. 3+-13 equals -10. Hence the total is really 5x = - 10.

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3 years ago

Oliver interviewed 30% of the 9th grade class and 70% of the 10th grade class at his school. Jenny interviewed 75% of the 9th gr

mixer [17]

Answer:

A . 36

Step-by-step 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 =

$\frac{70}{100} * \frac{176}{1}$

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 =

$\frac{30}{100} * \frac{176}{1}$

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 =

$\frac{75}{100} * \frac{140}{1}$

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 =

$\frac{25}{100} * \frac{140}{1}$

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

<h2>Therefore, there are 36 more 10th than 9th.</h2>

<h3>Extra Info:</h3>

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% = $\frac{30}{100}$ while, 70% = $\frac{70}{100}$

Now solve it;

$\frac{30}{100} + \frac{70}{100}$

Simplify; cancel bottom zero's;

$\frac{30}{1} + \frac{70}{1}$

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% = $\frac{25}{100}$ and, 75% = $\frac{75}{100}$