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One number is 2 more than 3 times another. Their sum is 22. Find the numbers.

Sagot :

iGreen
Make a system of equations.

[tex]\sf~x=3y+2[/tex]
[tex]\sf~x+y=22[/tex]

Re-arrange the 2nd equation:

[tex]\sf~x+y=22[/tex]

Subtract y to both sides:

[tex]\sf~x=-y+22[/tex]

Plug in -y + 22 for 'x' in the first equation.

[tex]\sf~x=3y+2[/tex]

[tex]\sf~-y+22=3y+2[/tex]

Subtract 3y to both sides:

[tex]\sf~-4y+22=2[/tex]

Subtract 22 to both sides:

[tex]\sf~-4y=-20[/tex]

Divide -4 to both sides:

[tex]\sf~y=\boxed{\sf5}[/tex]

Plug this into any of the two equations to find 'x':

[tex]\sf~x+y=22[/tex]

[tex]\sf~x+5=22[/tex]

Subtract 5 to both sides:

[tex]\sf~x=\boxed{\sf17}[/tex]

So one of the numbers is 5 and one of them is 17.
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