SOLUTION: the sum of two numbers is 53. if three times the smaller is one less than the larger, find the numbers. please show all work im lost

Question 280654: the sum of two numbers is 53. if three times the smaller is one less than the larger, find the numbers. please show all work im lost
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
First, lay out what you know or are told.
x = one number
y = another number
x + y = 53 :: given
.
Note that later work will be easier if we define y = 53 - x and substitute as needed.
.
x = smaller number :: our decision here is purely arbitrary
3x = three times the smaller number
.
y = larger number :: logically, it has to be
.
3x = y -1 :: 3 times the smaller number is one less than the larger number.
.
substituting for 'y'
.
3x = (53-x) -1
3x = 53 -x -1
3x = -x + 52
.
add 'x' to both sides
.
4x = 52
.
divide both sides by 4
.
x = 13
.
substituting once again
.
x + y = 53
13 + y = 53
y = 40
.
Answer:
The two numbers are 13 and 40.
Their sum is 53
Three times the smaller number is 3*13 = 39, which is one less than the larger number.
.
Done.
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