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Keisha the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 3 clients who did Plan A and 5 who did Plan B. On Saturday there were 12 clients who did Plan A and 2 who did Plan B. Keisha trained her Friday clients for a total of 9 hours and her Saturday clients for a total of 9 hours. How long does each of the workout plans last?

Respuesta :

Answer:

Plan A lasts 0.5 minutes

Plan B lasts 1.5 hours

Step-by-step explanation:

Let Plan A last [tex]a[/tex] hours, and Plan B last [tex]b[/tex] hours.

We have

[tex]\left \{ {{3a+5b=9} \atop {12a+2b=9}} \right.[/tex]

We'll multiply the top equation by 4, then subtract the second equation from it to get

[tex]18b=27\\b=1.5[/tex]

We'll substitute this back into the original first equation [tex]3a+5b=9[/tex] to get

[tex]3a+7.5=9\\3a=1.5\\a=0.5[/tex]

[tex]\therefore \left \{ {{a=0.5} \atop {b=1.5}} \right.[/tex]

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