SOLUTION: the larger of two numbers is 16 more than the smaller. when added together their sum is 6 less than 3 times the smaller. what are the numbers? (16 + a) + b = 3b -6

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Question 847821: the larger of two numbers is 16 more than the smaller. when added together their sum is 6 less than 3 times the smaller. what are the numbers?
(16 + a) + b = 3b -6


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Numbers a and b, a%3Cb.
b-a=16 and a%2Bb=-6%2B3a; in other words, you start with two equations.

Simplify the a+b equation.
a%2Bb-3a=-6
-2a%2Bb=-6
highlight_green%282a-b=6%29.

Put the a-b equation into the same form.
-a%2Bb=16
highlight_green%28a-b=-16%29.

You could have skipped most of that once you had the two equations translated from the description, and then continued with a substitution method to find a and b; but now you also have an equivalent system of equations for which the Elimination Method would be convenient.
-
Subtract one equation from the other to eliminate b:
2a-b-%28a-b%29=6-%28-16%29
... which will give you.....?