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
[tex]-13x/3 = 27.95*(-4/3)+23.40\\[/tex]
Simplifying, we get
[tex]-13x = 27.95*(-4)+23.4*3\\\\-13x = -41.6\\\\x=3.2[/tex]
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.
