SOLUTION: 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

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
RELATED QUESTIONS
The difference between two numbers is 12. iIf 2 is added to seven times the smaller... (answered by Pieter)

the difference between two numbers is 8. if 2 is added to the bigger number the result... (answered by TimothyLamb)

The difference between two numbers is 8; if 2 is added to the greater the result will be... (answered by algebra hello)

The difference between two numbers is 8, if 2 be added to the greater the result will be... (answered by macston)

The difference between two numbers is 12. If 20 is added to twice the larger number the... (answered by ankor@dixie-net.com)

The sum of two Numbers is -2. If twice the smaller number is added to three times the... (answered by checkley75)

When 1 is added to the difference between seven times a number and 7, the result is... (answered by addingup)

If 9 is subtracted from seven times a certain number, the result is the same as if 23 is... (answered by stanbon)

If one is subtracted from seven times a certain number the result is the same as if 31 is (answered by mananth)