If m varies directly as p, and m = 24 when p = 6, find m when p is 8.
Well, if m varies directly as p, it means that the ratio between m and p remains constant. So, we can set up a proportion to solve for m:
m/p = 24/6
To find m when p is 8, we can plug in the value of p into the proportion and solve for m:
m/8 = 24/6
Cross-multiplying gives us:
6m = 8 * 24
Now, let's do some math:
6m = 192
Dividing both sides by 6:
m = 32
So, when p is 8, m is equal to a whopping 32! That's quite a jump from the initial m value, isn't it?
To find the value of m when p is 8, we can use the direct variation formula:
m = kp, where k is the constant of variation.
Step 1: Use the given values to find the value of k.
We are given that m = 24 when p = 6.
Plugging these values into the formula:
24 = k * 6
Simplifying the equation:
24/6 = k
4 = k
Step 2: Use the value of k to find m when p is 8.
Using the formula:
m = kp
Plugging in the value of k (4) and the given value of p (8):
m = 4 * 8
m = 32
Therefore, when p is 8, m is equal to 32.
To find the value of m when p is 8, we first need to understand what it means for m and p to vary directly.
When two variables, m and p, vary directly, it means that they are related by a constant ratio. In other words, if you increase one variable by a certain amount, the other variable will also increase by that same amount, and vice versa. Mathematically, we can express this relationship as:
m = kp
where k is the constant of variation.
In this case, we are given that m = 24 when p = 6. We can use this information to find the value of k. Let's substitute these values into the equation:
24 = k * 6
To solve for k, we divide both sides of the equation by 6:
24/6 = k
Simplifying, we find that k = 4.
Now that we know the value of k, we can find m when p is 8 by substituting these values into the equation:
m = 4 * 8
Simplifying, we find that m = 32.
Therefore, when p is 8, m is equal to 32.
m varies directly as p ----> m = kp
when m=24,p=6
24 = k(6)
k = 4
so we know
m = 4p
sub in p = 8
or .... just use a simple ratio equation
8/6 = m/24
solve for m