## The sum of two integers is 33. The larger is 6 more than twice the smaller. Find the two integers.

Question

The sum of two integers is 33. The larger is 6 more than twice the smaller. Find the two
integers.

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1 year 2021-08-31T22:17:00+00:00 2 Answers 8 views 0

1. first we called x is the smaller number
next we have larger number is 2x+6
=>we have:2x+6+x=33
<=>x=9
so we have the larger number is 33-9=24

24 and 9

Step-by-step explanation:

Hi there!

Let x be equal to the larger integer.

Let y be equal to the smaller integer.

1) Construct equations

1. [tex]x+y=33[/tex] (The sum of two integers is 33)
2. [tex]x=6+2y[/tex] (The larger is 6 more than twice the smaller)

2) Solve for one of the integer

Isolate x in the first equation

[tex]x+y=33\\x=33-y[/tex]

Plug the first equation into the second

[tex]33-y=6+2y[/tex]

Combine like terms

[tex]33-6=2y+y\\27=3y\\9=y[/tex]

Therefore, the smaller integer is 9.

3) Solve for the other integer

[tex]x+y=33[/tex]

Plug in y (9)

[tex]x+9=33\\x=33-9\\x=24[/tex]

Therefore, the larger integer is 24.

I hope this helps!