Write an inequality and solve

Question

Samuel makes twice as much per hour as Kathy but Kathy works three times as many hours per week as Samuel 6 hours and the sum of their wages exceeds $480 how much does each of them make per hour

Answer 1

Let's say Samuel earns x dollars per hour. Since Samuel makes twice as much as Kathy per hour, Kathy earns (1/2)x dollars per hour.
Kathy works three times as many hours as Samuel, so Kathy works 3 * 6 = <<3*6=18>>18 hours per week.
Samuel works 6 hours per week.
The total wages earned by Samuel in a week are 6 * x = 6x dollars.
The total wages earned by Kathy in a week are 18 * (1/2)x = 9x dollars.
The sum of their wages exceeds $480, so 6x + 9x > 480.
Simplifying the inequality, 15x > 480.
Dividing both sides of the inequality by 15, we get x > 32.
Therefore, Samuel makes more than $32 per hour.
Kathy makes half as much as Samuel, so Kathy makes (1/2) * 32 = $<<1/2*32=16>>16 per hour. Answer: \boxed{16}.