a.
Friday:
[tex]30x + 20y = 910[/tex]
Saturday:
[tex]45x + 30y = 1365[/tex]
b.
[tex]30x + 20y = 910[/tex]
[tex]30x = 910 - 20y[/tex]
Divide both sides by 30:
[tex]x = \frac{910 - 20y}{30} [/tex]
Simplify the fraction:
[tex]x = \frac{91 - 2y}{3} [/tex]
(It is impossible to solve for specific values for x and y as seen in part c, so I'm not sure what the question is asking to solve for.)
c.
[tex]45x + 30y = 1365[/tex]
Substitute x = (91-2y)/3 in that equation (which is Saturday's equation)
[tex]45 \times \frac{91 - 2y}{3} + 30y = 1365[/tex]
[tex]15(91 - 2y) + 30y = 1365[/tex]
[tex]1365 - 30y + 30y = 1365[/tex]
[tex]1365 = 1365[/tex]
Hence, there is an infinite amount of solutions for x and y.
