Question

How do I do these problems? HELP! I added pics btw.

Answer 1

Answer:

Question 6: 6.8

Question 7: 8295

Step-by-step explanation:

Question 6:

Let's say that each hamburger costs x amount of dollars, and each soda costs y amount of dollars. For the first statement, we purchase 7 hamburgers (so 7 times x) and 3 sodas (3 times y) to add up to 27.95. As an equation, this means that 7x+3y=27.95. Similarly, for the second statement, 5x+4y=23.40.

Putting these two side by side, we get:

7x+3y=27.95

5x+4y=23.40

Using Gauss-Jordan elimination, we can multiply the first equation by -4/3 and then add that to the second equation, resulting in

$-13x/3 = 27.95*(-4/3)+23.40$

Simplifying, we get

$-13x = 27.95*(-4)+23.4*3\\\\-13x = -41.6\\\\x=3.2$

Question 7:

Take the number of students as x and the number of teachers as y. There are 35 times as many students as there are teachers, so 35y=x. We know that the students and teachers added up equal 8544-12=8532 (as 12 seats are empty in the auditorium that can seat 8544, 8532 must be occupied), so x+y= 8532. Since 35y=x, 35y+y+8532, 36y=8532, and y= 237. Since the number of students is equal to x, and x=35y, 35*y=35*237=8295 students.