To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each
customer and the average number of customers per hour. Create an inequality in standard form
that represents the restaurant owner's desired revenue.
Type the correct answer in each box. Use numerals instead of words.

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MrRoyal MrRoyal · Answer 1 · 2022-01-19T12:36:40+01:00

The inequality that represents the restaurant owner's desired revenue is [tex]x^2 +2x - 15 \le 0[/tex]

Inequalities are used to represent unequal expressions
Inequalities are represented by any of the following signs <, >, >= and <=

The inequality from the complete question is represented as:

[tex](10 + x \cdot 1) \cdot (16 - 2 \cdot x) \ge 130[/tex]

Evaluate the products, in the brackets

[tex](10 + x) \cdot (16 - 2x) \ge 130[/tex]

Expand the brackets

[tex]160 - 20x + 16x - 2x^2 \ge 130[/tex]

Evaluate the like terms

[tex]160 - 4x - 2x^2 \ge 130[/tex]

Divide through by 2

[tex]80 - 2x - x^2 \ge 65[/tex]

Rewrite the above inequality as:

[tex]- x^2 -2x + 80 \ge 65[/tex]

Collect like terms

[tex]- x^2 -2x + 80 -65 \ge 0[/tex]

[tex]- x^2 -2x + 15 \ge 0[/tex]

Multiply through by -1

[tex]x^2 +2x - 15 \le 0[/tex]

Hence, the inequality that represents the restaurant owner's desired revenue is [tex]x^2 +2x - 15 \le 0[/tex]