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?

Algebra.Com
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): You can put this solution on YOUR website!
.
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)
—


RELATED QUESTIONS

The sum of three numbers is 10. The sum of twice the first​ number, 5 times the... (answered by MathLover1)
The sum of three numbers is 10. The sum of twice the first​ number, 4 times the... (answered by ikleyn)
There are two mystery numbers. The sum of 3 times the first number and 7 times the second (answered by JulietG)
The sum of three numbers is 10. The sum of twice the first number, 3 times the second... (answered by ankor@dixie-net.com)
the sum of three numbers is 20.The second number is 4 times the first, and the sum of the (answered by checkley71)
The sum of three numbers is 110. The second number is 10 less than the first. The third... (answered by MathLover1)
The sum of three numbers is 10. The sum of twice the first​ number, 4 times the... (answered by MathLover1,MathTherapy)
The sum of 4 times the first number and three times the second number is 15. The... (answered by Cromlix)
The sum of three numbers is 92. The second number is 10 more than the first. The third... (answered by josgarithmetic)