SOLUTION: Please help me with this. The difference between two numbers is three. The sum of twice the larger and one-half the smaller is 36. Find the numbers.

Question 1190041: Please help me with this. The difference between two numbers is three. The sum of twice the larger and one-half the smaller is 36. Find the numbers.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = smaller number
x+3 = larger number
This is because of the phrasing
"The difference between two numbers is three"

In other words, the gap from x to x+3 is exactly 3 units.

Then we turn to the next bit of info your teacher gave you:
"The sum of twice the larger and one-half the smaller is 36"

That translates to this equation:
2*(larger) + 0.5*(smaller) = 36
2*(x+3) + 0.5*(x) = 36
where I used 0.5 in place of the fraction 1/2

Let's solve for x
2*(x+3) + 0.5*(x) = 36
2x+6 + 0.5x = 36
2.5x+6 = 36
2.5x = 36-6
2.5x = 30
x = 30/2.5
x = 12 is the smaller value
x+3 = 12+3 = 15 is the larger value

As a check,
2*(larger) + 0.5*(smaller) = 36
2*(15) + 0.5*(12) = 36
30 + 6 = 36
36 = 36
which works out. The answers are confirmed.

Answers:
Smaller number = 12
Larger number = 15

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