SOLUTION: The sum of two numbers is 15 less than twice the first number. Their difference is 5 less than twice the second number. Find each of the numbers. Enter the larger number in the ans

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The sum of two numbers is 15 less than twice the first number. Their difference is 5 less than twice the second number. Find each of the numbers. Enter the larger number in the ans      Log On


   



Question 762688: The sum of two numbers is 15 less than twice the first number. Their difference is 5 less than twice the second number. Find each of the numbers. Enter the larger number in the answer box below
Found 2 solutions by lordshubham, Stitch:
Answer by lordshubham(4) About Me  (Show Source):
You can put this solution on YOUR website!
let 1 no be x
other no be y
x+y=15-2x
3x+y=15.....(I)
x-y=5-2y
x+y=5.......(II)
Solving I and II
x= 5 and y= 0
therfore two numbers are 5 and 0

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Equation 1: A+%2B+B+%2B+15+=+2A
Equation 2: A+-+B+%2B+5+=+2B
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First you need to solve one of the equations for one variable.
I chose the second equation.
Equation 2: A+-+B+%2B+5+=+2B
Add B to both sides.
A+%2B+5+=+3B
Subtract 5 from both sides.
A+=+3B+-+5
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Now plug (3B - 5) into equation 1 for A.
Equation 1: A+%2B+B+%2B+15+=+2A
%283B+-+5%29+%2B+B+%2B+15+=+2%2A%283B+-+5%29
Simplify.
3B+-+5+%2B+B+%2B+15+=+6B+-+10
Combine like terms.
4B+%2B+10+=+6B+-+10
Subtract 4B from both sides.
10+=+2B+-+10
Add 10 to both sides.
20+=+2B
Divide both sides by 2.
highlight%2810+=+B%29
Now plug 10 in for B and solve for A.
A+=+3B+-+5
A+=+3%2A%2810%29+-+5
A+=+30+-+5
highlight_green%28A+=+25%29