The sum of two numbers is 37/6. One of these numbers is greater than the other by 2. What are these numbers?
Well, isn't it fascinating how numbers can be all "juicy" with fractions and differences? It's like a math smoothie!
Let's call the smaller number "x" and the larger number "x + 2" (because the larger number is greater by 2). Now we know the sum of these two numbers is 37/6.
So, x + (x + 2) = 37/6. Are you ready to start this "math smoothie" party?
Let's simplify this equation by combining like terms: 2x + 2 = 37/6.
Now, let's make those fractions shake! We can multiply both sides of the equation by 6 to get rid of that pesky denominator. Are you dancing with excitement yet?
After multiplying everything, we end up with 12x + 12 = 37. Almost there!
Now, let's bring more treats to the party by subtracting 12 from both sides: 12x = 37 - 12. Razzle-dazzle, things are getting interesting!
We simplify further to get 12x = 25. Can you feel the tension building?
Finally, we divide both sides by 12 to isolate x: x = 25/12. We have invited a fraction to our party!
Now, let's find the larger number by adding 2 to x: x + 2 = 25/12 + 2. Our party is getting crowded with fractions!
To simplify this further, we need a common denominator. Let's get our fractions dancing together: x + 2 = 25/12 + 24/12.
Adding the fractions, we get x + 2 = 49/12. Oh boy, our fractions are really tearing up the dance floor now!
To finalize things, let's subtract 2 from both sides: x = 49/12 - 2. Our fractions are taking a final bow!
After subtracting, we get x = 25/12, which is the smaller number. And the larger number is x + 2, which simplifies to (25/12) + 2.
So, the smaller number is 25/12 and the larger number is (25/12) + 2. Voila!
Let's assume the smaller number is x.
According to the problem, the other number is greater than x by 2, so the larger number is x + 2.
The sum of the two numbers is given as 37/6, so we can write the equation:
x + (x + 2) = 37/6
Combining like terms:
2x + 2 = 37/6
To get rid of the fraction, we can multiply both sides of the equation by 6:
6(2x + 2) = 37
Distribute the 6:
12x + 12 = 37
Subtract 12 from both sides:
12x = 37 - 12
12x = 25
Divide both sides by 12:
x = 25/12
So, the smaller number is 25/12.
To find the larger number, we substitute x back into the expression x + 2:
25/12 + 2 = 25/12 + 24/12 = 49/12
Therefore, the larger number is 49/12.
To find the two numbers, let's assign variables to represent them. Let's call one number "x" and the other number "y".
According to the information given, we know two things:
1) The sum of the two numbers is 37/6: x + y = 37/6.
2) One of the numbers is greater than the other by 2: x = y + 2.
Now we can solve this system of equations to find the values of x and y.
Substituting the value of x from the second equation into the first equation, we have:
(y + 2) + y = 37/6.
Combine like terms on the left side:
2y + 2 = 37/6.
To eliminate the fraction, we can rewrite 37/6 as a decimal by dividing 37 by 6:
2y + 2 = 6.16 (rounded to two decimal places).
Next, subtract 2 from both sides of the equation:
2y = 6.16 - 2 = 4.16.
Finally, divide both sides of the equation by 2:
y = 4.16 / 2 = 2.08 (rounded to two decimal places).
Now that we have found the value of y, we can substitute it back into the second equation to find x:
x = 2.08 + 2 = 4.08 (rounded to two decimal places).
Therefore, the two numbers are approximately x = 4.08 and y = 2.08.
5/6
x + x+2 = 37/6
now finish it off