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Question 3478: The difference between two numbers is 12. If 2 is added to seven times the smaller number, the result is the same as if 2 is subtracted from three times the larger number. Find the numbers.
Answer by Pieter(35)   (Show Source):
You can put this solution on YOUR website! the difficulty of this exercise is to transform the text ito symbols.
The difference between two numbers is 12: a-b = 12 (I)
(then we choose a the largest number and b the smallest
If 2 is added to seven times the smaller number, the result is the same as if 2 is subtracted from three times the larger number: this becomes:
7b+2 = 3a-2 (II)
from (I) we get: a = 12+b and this we fill in into (II), this method is called 'substituting' because you change a part in one equation with information you get from another one. So we get:
7b+2 = 3(12+b)-2
7b+2 = 36+3b-2
7b-3b = 36-2-2
4b=32 or b=32/4= 8
and we know a = 12+b = 12+8 = 20
check: 20-8=12 (I) ==>ok
2+7*8 = 3*20-2 ==>ok
Contact me if you have any questions
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