One number is greater than another by 40/11. If the smaller number is less than 47/22 by 1/2, find the numbers.
small = 47/22 - 1/2
large = small + 40/11
small = 36/22
large = 116/22
Let's assume the smaller number is x.
According to the given information, the larger number is 40/11 greater than the smaller number. Therefore, the larger number is x + 40/11.
It is also given that the smaller number is 1/2 less than 47/22. Thus, we can write the equation:
x = 47/22 - 1/2
To simplify the equation, we need to find a common denominator for 22 and 2, which is 44. We get:
x = 47/22 - 11/44
Combining the fractions on the right side, we have:
x = (47 - 11*2) / 22
Simplifying further, we get:
x = (47 - 22) / 22
x = 25 / 22
Therefore, the smaller number is 25/22.
Now we can find the larger number:
Larger number = Smaller number + 40/11
Larger number = 25/22 + 40/11
To find a common denominator, we multiply 22 by 2 to get 44:
Larger number = 25/22 + (40*2) / (11*2)
Larger number = 25/22 + 80 / 22
Combining the fractions, we have:
Larger number = (25 + 80) / 22
Larger number = 105 / 22
Therefore, the larger number is 105/22.
So, the smaller number is 25/22 and the larger number is 105/22.
To find the numbers, let's assign variables to them. Let's say the smaller number is "x" and the larger number is "y".
Based on the given information, we have two equations:
1) y = x + 40/11 (One number is greater than another by 40/11)
2) x = 47/22 - 1/2 (The smaller number is less than 47/22 by 1/2)
Let's solve for "x" in the second equation:
x = 47/22 - 1/2
To add fractions, we need to find a common denominator:
x = (47/22) - (11/22)
x = 36/22
x = 18/11
Now that we know the value of "x", we can substitute it back into the first equation to find "y":
y = x + 40/11
y = 18/11 + 40/11
y = 58/11
Therefore, the two numbers are:
Smaller number (x) = 18/11
Larger number (y) = 58/11