The variables a and b are inversely proportional. When the sum of a and b is 24, their difference is 6. What is b when a equals 5?
24-a = a-6
a = 15, b=9
ab=k, so we want
5b = 15*9
b = 27
Well, I can see that "a" and "b" have quite the relationship going on. They're inversely proportional, which means as one goes up, the other goes down. It's like a love-hate kind of thing.
Now, let's do some math. We know that when the sum of "a" and "b" is 24, their difference is 6. So we can set up two equations:
a + b = 24
a - b = 6
Now, you want to find out what "b" is when "a" equals 5. It's like a math puzzle!
Let's use our clown logic to solve this one. We'll start by substituting the value of "a" into the first equation:
5 + b = 24
Then, we can solve for "b" by subtracting 5 from both sides:
b = 24 - 5
Using our amazing clown math skills, we find that b equals 19! Ta-da!
To solve this problem, you can use the method of solving systems of equations.
Step 1: Set up the equation for the inverse proportion.
Since a and b are inversely proportional, their product remains constant: a * b = k, where k is a constant.
Step 2: Set up the equation representing the given conditions.
We are given that the sum of a and b is 24, so a + b = 24.
We are also given that their difference is 6, so a - b = 6.
Step 3: Solve the system of equations.
To do this, we can use the method of substitution. Solve one equation for one variable and substitute it into the other equation.
From the equation a + b = 24, we can solve for a:
a = 24 - b.
Substitute this expression for a into the equation a - b = 6:
(24 - b) - b = 6.
Simplify the equation:
24 - 2b = 6.
Step 4: Solve for b.
Subtract 24 from both sides of the equation:
-2b = 6 - 24,
-2b = -18.
Divide both sides of the equation by -2:
b = (-18) / (-2),
b = 9.
Therefore, when a equals 5, b equals 9.
To solve this problem, we need to set up equations representing the given information.
First, we are told that the variables a and b are inversely proportional, which means that their product is constant. Let's call this constant k.
So, we have the equation a * b = k.
Next, we are given two additional conditions:
1. The sum of a and b is 24: a + b = 24.
2. Their difference is 6: a - b = 6.
Now, let's solve these equations to find the values of a and b.
From the equation a + b = 24, we can isolate a by subtracting b from both sides:
a = 24 - b ----(1)
From the equation a - b = 6, we can isolate a by adding b to both sides:
a = b + 6 ----(2)
Now, we can set these two equations equal to each other:
24 - b = b + 6
Simplify the equation:
24 = 2b + 6
Subtract 6 from both sides:
18 = 2b
Divide both sides by 2:
9 = b
So, when a equals 5, b equals 9.