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Sagot :
Using a system of equations, it is found that both workout plans last 45 minutes.
For the system, we have that:
- x is the length of a Plan A workout.
- y is the length of a Plan B workout.
On Monday there were 5 clients who did Plan A and 3 who did Plan B, for a total of 6 hours, hence:
[tex]5x + 3y = 6[/tex]
On Tuesday there were 7 clients who did Plan A and 9 who did Plan B, for a total of 12 hours, hence:
[tex]7x + 9y = 12[/tex]
The system is:
[tex]5x + 3y = 6[/tex]
[tex]7x + 9y = 12[/tex]
Multiplying the first equation by -3:
[tex]-15x - 9y = -18[/tex]
[tex]7x + 9y = 12[/tex]
Adding them:
[tex]-8x = -6[/tex]
[tex]8x = 6[/tex]
[tex]x = \frac{3}{4}[/tex]
In minutes, x = 45 minutes.
Then:
[tex]9y = 12 - 7x[/tex]
[tex]9y = 12 - 7(0.75)[/tex]
[tex]y = \frac{12 - 7(0.75)}{9}[/tex]
[tex]y = 0.75[/tex]
Also 45 minutes.
A similar problem, also solved using a system of equations, is given at https://brainly.com/question/14183076
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