Write an inequality and solve
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
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}.
Let's assign variables to represent the wages per hour for Samuel and Kathy. Let's say Samuel's wage per hour is "s" and Kathy's wage per hour is "k".
According to the given information, Samuel makes twice as much per hour as Kathy, hence we can write the first inequality as:
s = 2k
Additionally, Kathy works three times as many hours per week as Samuel, so we can write the second inequality as:
3(6)k + 6s > 480
To solve these equations simultaneously, let's substitute the value of s from the first inequality into the second inequality:
3(6)k + 6(2k) > 480
Simplifying the equation further:
18k + 12k > 480
30k > 480
Dividing both sides of the inequality by 30:
k > 16
So Kathy's wage per hour is greater than $16.
To find the value of s, we can substitute the value of k in the first inequality:
s = 2(16)
s = 32
Therefore, Samuel's wage per hour is $32.
To solve this problem, let's assign variables to the unknown quantities. Let's say Samuel makes $x per hour, and Kathy makes $y per hour.
From the information given, we know that Samuel makes twice as much per hour as Kathy. This can be represented as:
x = 2y (Equation 1)
We are also told that Kathy works three times as many hours per week as Samuel. If Samuel works 6 hours, then Kathy works 3 times that, which is 3 * 6 = 18 hours.
Now, we need to find the sum of their wages, which exceeds $480. The total amount of money Samuel makes in 6 hours is 6 * x, and the total amount of money Kathy makes in 18 hours is 18 * y. The sum of their wages can be represented as:
6x + 18y > 480 (Inequality 2)
To solve this system of equations, we can use substitution. Let's substitute the value of x from Equation 1 into Inequality 2.
6(2y) + 18y > 480
12y + 18y > 480
30y > 480
y > 480/30
y > 16
So Kathy's hourly wage, y, is greater than $16.
Now, let's substitute the value of y back into Equation 1 to solve for x:
x = 2(16)
x = 32
Therefore, Samuel's hourly wage, x, is $32.
In conclusion, Samuel makes $32 per hour, and Kathy makes more than $16 per hour.