SOLUTION: the first number increased by 7 is equal to twice a second number. the second number increased 9 is equal to three times the first. find these two numbers

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Question 138961: the first number increased by 7 is equal to twice a second number. the second number increased 9 is equal to three times the first. find these two numbers
Answer by Earlsdon(6294) (Show Source):
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Let a = the first number and b = the second number.
From the problem description, you can write:
1) a+7 = 2b "The first number increased by 7 is equal to twice the second number."
2) b+9 = 3a "The second number increased by 9 is equal to thrice the the first number."
Solve the first equation for a and substitute this into the second equation, then solve for b.
1) a = 2b-7
2)b+9 = 3(2b-7) Simplify.
b+9 = 6b-21 Subtract b from both sides.
9 = 5b-21 Add 21 to both sides.
30 = 5b Divide both sides by 5
b = 6
a = 2b-7
a = 2(6)-7
a = 12-7
a = 5
The two numbers are: 5 and 6