SOLUTION: The sum of 4 times the first number and 10 times the second number is 48. The sum of 10 times the first number and 4 times the second number is 36. What are the two numbers?

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Question 1071619: The sum of 4 times the first number and 10 times the second number is 48. The sum of 10 times the first number and 4 times the second number is 36. What are the two numbers?

Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52803)   (Show Source):
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4x + 10y = 48, (1) 10x + 4y = 36. (2) Multiply equation (1) by 5 (both sides). Multiply equation (2) by 2 (both sides). You will get 20x + 50y = 240, (3) 20x + 8y = 72. (4) Subtract eq(4) from eq(3) (both sides). You will get 42y = 240-72 = 168 ---> y = = 4. Can you complete the solution from this point on your own ?

The method I applied here is called the Elimination method.

See the lessons
    - Solution of the linear system of two equations in two unknowns by the Substitution method
    - Solution of the linear system of two equations in two unknowns by the Elimination method
    - Solution of the linear system of two equations in two unknowns using determinant
    - Geometric interpretation of the linear system of two equations in two unknowns
    - Solving word problems using linear systems of two equations in two unknowns
    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!

4x+10y = 48 (1) 10x+4y = 36 (2) Multiply both sides of (1) by 10, and both sides of (2) by 4: 40x + 100y = 480 (1') 40x + 16y = 144 (2') Subtract (2') from (1') to get: 0x + 84y = 336 �> y = 336/84 = 4. Using 4x + 10y = 48 and y=4 �> 4x + 10(4) = 48 �> 4x = 48-40 �> 4x = 8 �> x=2 � Ans: and � Check: 4(2) + 10(4) = 8 + 40 = 48 (ok, eqn 1 works) 10(2) + 4(4) = 20 + 16 = 36 (ok, eqn 2 works as well) �