SOLUTION: The sum of two numbers is 145. When the smaller number is decreased by two and the larger number is increased by 1, their ratio will be 2:7. What are the numbers.

Question 811694: The sum of two numbers is 145. When the smaller number is decreased by two and the larger number is increased by 1, their ratio will be 2:7. What are the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two number a & b
Write an equation for each statement
:
The sum of two numbers is 145.
a + b = 145, (a is the larger number)
a = (145-b)
:
When the smaller number is decreased by two and the larger number is increased by 1,
their ratio will be 2:7.
=
Cross multiply
7(b-2) = 2(a+1)
7b - 14 = 2a + 2
7b = 2a + 2 + 14
7b = 2a + 16
Replace a with (145-b)
7b = 2(145-b) + 16
7b = 290 - 2b + 16
7b + 2b = 306
9b = 306
b = 306/9
b = 34
then
a = 145 - 34
a = 111
:
:
See if that works out
=
reduces to

:

RELATED QUESTIONS
The sum of two numbers is 16. Three times the larger number decreased by the smaller... (answered by macston)

The sum of two numbers is 18. Twice the smaller number decreased by three equals the... (answered by addingup)

The sum of two numbers is 18. Twice the smaller number decreased by three equals the... (answered by ankor@dixie-net.com)

The sum of two numbers is 18. Twice the smaller number decreased by three equals the... (answered by MathLover1)

7. The sum of two numbers is 17 and the sum of their square is 145. Find the larger... (answered by stanbon)

The sum of two numbers is 17 and the sum of their square is 145. Find the larger number. (answered by checkley71,solver91311)

The larger of two numbers is equal to three times the smaller number, the smaller number... (answered by TimothyLamb)

The sum of two numbers is 45. if three time the larger number is increased by four times... (answered by checkley79)

the sum of the two numbers is 39. When the smaller number is doubled and the larger is... (answered by richwmiller)