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A high school sports team is ordering sports drinks online from a company. The price of sports drinks varies, based on the number of drinks purchased. For orders of 50 or fewer sports drinks, the price is $0.80 per drink, plus $10 shipping and handling. When more than 50 sports drinks are ordered, the price is $0.70 per drink, plus $15 shipping and handling. What is the maximum amount of sports drinks you can purchase for $85?
88
94
100
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Sagot :

MrRoyal

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

Read more about functions at:

https://brainly.com/question/20286983

Aviatzi

Answer: The maximum amount of sports drinks you can purchase for $85 is 100

Step-by-step explanation:

When you solve for x using the equations

85=10+0.8x and 85=15+0.7x

you get 93.7 and 100

93.7 rounded to the nearest whole number is 94

100>94

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