Berta is planning a party for her friends. the room rental cost is $50 plus an additional $3 per person to cover food costs. berta has saved up $100 dollars. what is the maximum number of people that can attend her party? identify the inequality to solve and the maximum number of people. a. 3x+50_< 100; 16 people b. 3x+50_< 100; 50/3 people c. 3x+50_> 100; 17 people d. 3x_< 100; 33 people

  A. 3x+50 ≤ 100; 16 people

Step-by-step explanation:

If x represents the number of people at Berta's party, then the cost of food is 3x. Added to the $50 cost of room rental, the total charge Berta must pay will be ...

  3x +50

She wants this to be at most $100, so her inequality is ...

  3x +50 ≤ 100

Berta can solve this by subtracting 50, then dividing by 3.

  3x ≤ 50

  x ≤ 16 2/3

Since x represents a number of people, and it is not possible (or desirable) to have 2/3 of a person show up, the maximum number of people that can attend Berta's party is 16.

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15