SOLUTION: The sum of two numbers is 12. Three times the larger is 6 more than 7 times the smaller. Find the two numbers.

Question 237449: The sum of two numbers is 12. Three times the larger is 6 more than 7 times the smaller. Find the two numbers.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 12. Three times the larger is 6 more than 7 times the smaller. Find the two numbers.
------------------
Equations:
x + y = 12
3x = 7y + 6
-------------------
Multiply 1st by 3 and Rearrange both equations:
3x + 3y = 36
3x - 7y = 6
--------------------
Subtract the 2nd from the 1st and solve for "y":
10y = 30
y = 3
----------------------------
Substitute into x+y = 12 to solve for "x":
x + 3 = 12
x = 9
----------------------------
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the smaller number. Let represent the larger number. Then

Solve the system. Hint, Solve the first equation for either of the variables and then use the substitution method.

John

RELATED QUESTIONS
The larger of two numbers is eight more than three times the smaller number. The sum of... (answered by Boreal,greenestamps)
The larger of two numbers is one more than twice the smaller. The sum of the numbers is... (answered by mananth)
The larger of two numbers is 8 more than twice the smaller. The sum of the numbers is 10... (answered by mananth)
The larger of two numbers is 8 more than twice the smaller. The sum of the numbers is 10... (answered by josgarithmetic)
the larger of two numbers is 16 more than the smaller. when added together, the sum of... (answered by Maths68)
The larger of two numbers is three more than five times the smaller. If the sum of the... (answered by RAY100)
The sum of two numbers is 23. the difference between three times the smaller and seven is (answered by nerdybill)
Number Problem: The sum of two numbers is 70. The larger number is two more than three... (answered by rfer)
Please help me solve this question please: The larger of two numbers is 6 less than 3... (answered by mathslover)