Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf

She writes the expression
(x - 5) (50 - 2x) to represent her profit based on the price per scarf, x

Drag inequalities to the table to
match the description in each row.

a) 5<x<25

b) x≤5 or x≥25

c) x≥5 and x≤25

Step-by-step explanation:

Given the expression the

(x - 5) (50 - 2x) to represent sofie profit based on the price per scarf, x.

a) If Sofie's profit is increasing, them the expression for her profit must be greater than zero as shown.

(x - 5) (50 - 2x)> 0

Solving the inequality:

x-5>0 and 50-2x>0

If x-5>0

x > 5 or 5<x... (1)

Similarly when 50-2x>0

50-2x>0

50>2x

Dividing both sides by 2:

50/2>2x/2

25>x or x<25 ...(2)

Combining 1 and 2

5<x<25

b) if Sofie's profit is decreasing, the profit function must be less than or equal to zero as shown;

(x - 5) (50 - 2x)≤0

Solving the inequality

x-5≤0 and 50-2x≤0

x≤5 and 50≤2x

x≤5 or 25≤x

x≤5 or x≥25

c) If Sofia is not making profit then, the function (x - 5) (50 - 2x) is equal to zero i.e

(x - 5) (50 - 2x) = 0

x - 5 = 0 or 50-2x =0

x = 5 and 50 = 2x

x = 5 and x = 25

x≥5 and x≤25