two numbers differ by three and their quotient is 3/4. the larger number is? i not get how to do this.
X-3/x =3/4
Multiply 4 for the left side and right x
4x-12=3x
Make it equal 0
1x - 12 =0
And solve
x=12
thanks very much damon :)
Well, it seems we have a numerical mystery on our hands! Let's see if we can solve it while keeping our sense of humor intact.
Let's call the larger number "X" and the smaller number "Y". Since we know that the two numbers differ by three, we can say that X = Y + 3. Keep that equation in mind, it'll come in handy.
Now, we're given another piece of information: the quotient (which is just a fancy word for division) of the two numbers is 3/4. In other words, X/Y = 3/4.
Here comes the fun part - let's put our equations into action! Remember that X = Y + 3, so we can substitute that into the second equation.
(Y + 3) / Y = 3/4
Now, cross-multiplying should make things a bit easier. Let's multiply both sides of the equation by Y to clear out the denominator:
4(Y + 3) = 3Y
Now, distribute that 4 on the left side:
4Y + 12 = 3Y
Subtract 3Y from both sides:
Y + 12 = 0
Well, that seems a bit strange, doesn't it? It looks like the numbers we're dealing with are a bit out of this world. It seems we've made a mistake somewhere along the way or perhaps there's a bit more to this problem than meets the eye.
I must apologize for not being able to give you a clear answer. It seems the numbers are engaging in a little numerical mischief and have led us astray. Maybe we should recruit a math whiz to help solve this real puzzler!
To find the larger number, we can set up a system of equations based on the given information.
Let's say the two numbers are x and y, where x is the larger number. We are given two pieces of information:
1. "Two numbers differ by three": This means that the difference between the two numbers is 3. So we can write the equation as:
x - y = 3
2. "Their quotient is 3/4": This means that the division of the two numbers gives us a quotient of 3/4. So we can write the equation as:
x / y = 3/4
Now we can solve this system of equations to find the values of x and y.
One way to solve this is by substitution. Rearrange the first equation to solve for x:
x = y + 3
Now substitute this expression for x in the second equation:
(y + 3) / y = 3/4
Next, cross multiply to get rid of the fractions:
4(y + 3) = 3y
Expand the left side:
4y + 12 = 3y
Subtract 3y from both sides:
y + 12 = 0
Subtract 12 from both sides:
y = -12
Now substitute this value back into the first equation to find x:
x = -12 + 3
x = -9
So the larger number is -9.
n and (n+3)
n/(n+3) = 3/4
4 n = 3 n + 9
n = 9
n+3 = 12