SOLUTION: the larger of two numbers is 5 less than twice the smaller number. the sum of the two numbers is 28. what are the numbers?

Question 234152: the larger of two numbers is 5 less than twice the smaller number. the sum of the two numbers is 28. what are the numbers?
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
We have two equations in two variables in this case.
Let y = larger number
Let x = smaller number
The larger of two numbers is 5 less than twice the smaller number. This can be written as y = 2x - 5.
The sum of the two numbers is 28. This can be written as x + y = 28
Here are the two equations:
y = 2x - 5...equation A
x + y = 28...equation B
I will replace y in equation B with its value given in equation A to find x.
x + (2x - 5) = 28
3x - 5 = 28
3x = 28 + 5
3x = 33
x = 33/3
x = 11
The smaller number is 11.
To find y, let x = 11 in either equation A or B (your choice) and solve for y.
I will use x + y = 28 to find y.
Let x = 11
11 + y = 28
y = 28 -11
y = 17
The larger nuber is 17.

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