Question
A and B are positive whole numbers. A is less than B. If the sum of a and B a 37, and 9/A=B/30
Answers
GPT 3.5
The sum of A and B is 37, so we can write this as:
A + B = 37
We are also told that:
9/A = B/30
We can rearrange the second equation to get:
B = 30(9/A)
Now we can substitute this expression for B into the first equation:
A + 30(9/A) = 37
Multiplying through by A to get rid of the fraction:
A^2 + 270 = 37A
Rearranging this equation:
A^2 - 37A + 270 = 0
We can factor this equation:
(A - 27)(A - 10) = 0
So either A = 27 or A = 10. Since A is less than B, A must be 10 and B must be 27.
Therefore, A = 10 and B = 27.
A + B = 37
We are also told that:
9/A = B/30
We can rearrange the second equation to get:
B = 30(9/A)
Now we can substitute this expression for B into the first equation:
A + 30(9/A) = 37
Multiplying through by A to get rid of the fraction:
A^2 + 270 = 37A
Rearranging this equation:
A^2 - 37A + 270 = 0
We can factor this equation:
(A - 27)(A - 10) = 0
So either A = 27 or A = 10. Since A is less than B, A must be 10 and B must be 27.
Therefore, A = 10 and B = 27.