Suppose y varies jointly with x and z, and x = 4 when y = 8 and z = -2.What is the value of x when y = 12 and z = 3?
A. -4
B. 4
C. 15
D. 9
y = kxz
8 = k(-2)(4)
8 = -8k
k = -1
y = -3x
12 = -3x
x = -4
Answer is A
To find the value of x when y = 12 and z = 3, we need to use the concept of joint variation. When two variables vary jointly with another variable, it means that their product is constant.
In this scenario, y varies jointly with x and z. So we can write the equation as:
y = k * x * z,
where k is the constant of variation.
To find the value of k, we need to use the given information. It states that when x = 4, y = 8, and z = -2. Plugging these values into the equation, we get:
8 = k * 4 * (-2).
Simplifying:
8 = -8k.
Dividing both sides by -8:
k = -1.
Now that we have the value of k, we can find the value of x when y = 12 and z = 3:
12 = -1 * x * 3.
Simplifying:
12 = -3x.
Dividing both sides by -3:
x = -4.
Therefore, the value of x when y = 12 and z = 3 is -4. Hence, the correct answer is A.
To find the value of x when y = 12 and z = 3, we can use the concept of joint variation.
Joint variation can be expressed as:
y = k * x * z
where k is the constant of variation.
We can find the value of k by using the given equation when x = 4, y = 8, and z = -2:
8 = k * 4 * (-2)
Simplifying the equation, we get:
8 = -8k
Dividing both sides by -8, we find:
k = -1
Now, we can substitute the values of k, y, and z into the equation and solve for x when y = 12 and z = 3:
12 = -1 * x * 3
Simplifying the equation, we get:
12 = -3x
Dividing both sides by -3, we find:
x = -4
Therefore, the value of x when y = 12 and z = 3 is -4. Answer choice A is correct.