Question

The larger of two numbers is 1 more than twice the smaller. The sum of the numbers is 20 less than three times the larger. Find the numbers.

I NEED help please. I'm getting extremely frustrated!!

Answer 1

13 and 6

Explanation:

Let x = larger number

Let y = smaller number

The larger of two numbers is: x =

one more than twice the smaller: 2y + 1

x = 2y + 1 {equation 1}

The sum of the numbers is: x + y =

20 less than three times the larger: 3x - 20

x + y = 3x - 20

This can be simplified. Subtract 3x from both sides.

x - 3x + y = -20

-2x + y = -20 {equation 2}

Since we already know from equation 1 that x=2y+1, substitute that into equation 2

and solve for y:

-2(2y+1) + y = -20

-4y - 2 + y = -20

-3y - 2 = -20

-3y = -18

y = -18/(-3)

y = 6

x = 2y+1 = 2(6)+1 = 12 + 1 = 13

Your numbers are 13 and 6

Answer 2

Let x be the larger number; Let y be the smaller number.
EQUATIONS:
x-2y=1
x+y+20=3x
---------
Rewrite as
x-2y=1
2x-y=20
==========

Multiply the 1st equation by 2 to get:
2x-4y=2
Subtract this result from the 1st equation to get:
3y=18
y=6
Substitute that into the 1st equation to get:
x-2*6=1
x=13
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Solution: x=13; y=6