Answer:
Session A = 1.25 hours
Session B = 0.5 hours
Step-by-step explanation:
Given
Plans: A and B
Friday can be expressed as: 4A + 8B
Saturday can be expressed as: 2A + 3B
Total Time:
Friday = 9 hours
Saturday = 4 hours
Required
Determine time for each session (A and B)
The question illustrates simultaneous equation and the equations are;
[tex]4A + 8B = 9[/tex]
[tex]2A + 3B = 4[/tex]
Multiply the second equation by 2
[tex]2(2A + 3B = 4)[/tex]
[tex]4A + 6B = 8[/tex]
Subtract this from the first equation:
[tex](4A + 8B = 9) - (4A + 6B = 8)[/tex]
[tex]4A - 4A + 8B -6B = 9 - 8[/tex]
[tex]8B -6B = 1[/tex]
[tex]2B = 1[/tex]
Solve for B
[tex]B= \frac{1}{2}[/tex]
[tex]B = 0.5\ hours[/tex]
Substitute [tex]B= \frac{1}{2}[/tex] in [tex]2A + 3B = 4[/tex]
[tex]2A + 3(\frac{1}{2}) = 4[/tex]
[tex]2A + \frac{3}{2} = 4[/tex]
Solve for 2A
[tex]2A = 4 - \frac{3}{2}[/tex]
[tex]2A = \frac{8 - 3}{2}[/tex]
[tex]2A = \frac{5}{2}[/tex]
Solve for A
[tex]A = \frac{5}{2} * \frac{1}{2}[/tex]
[tex]A = \frac{5}{4}[/tex]
[tex]A = 1.25\ hours[/tex]
