The amount of drinks is a linear function of the number of drinks. The maximum amount that can be purchased is 100 soft drinks.
Let
[tex]y \to[/tex] amount of drinks
[tex]x \to[/tex] number of drinks
For drinks not more than 50
[tex]y = 10 + 0.8x[/tex]
For drinks more than 50.
[tex]y = 15 + 0.7x[/tex]
For a purchase of $85, it means that:
[tex]y = 85[/tex]
So, we solve for x in both equations.
[tex]y = 10 + 0.8x[/tex]
[tex]85 = 10 + 0.8x[/tex]
Collect like terms
[tex]0.8x = 85-10[/tex]
[tex]0.8x = 75[/tex]
Divide through by 0.8
[tex]x = 93.75[/tex]
[tex]x = 94[/tex] --- approximated
[tex]y = 15 + 0.7x[/tex]
[tex]85 =15 + 0.7x[/tex]
Collect like terms
[tex]0.7x = 85 - 15[/tex]
[tex]0.7x = 70[/tex]
Divide by 0.7
[tex]x = 100[/tex]
By comparing both values:
[tex]x = 100[/tex]
[tex]x = 94[/tex]
[tex]100 > 94[/tex]
Hence, the maximum amount that can be purchased is 100
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