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The larger of two numbers is eight more than three times the smaller number. The sum of the two numbers is fifty-two. Find the two numbers.

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LammettHash
Let [tex]x[/tex] be the larger number and [tex]y[/tex] the smaller number.

The first sentence translates to [tex]x=8+3y[/tex]. The second translates to [tex]x+y=52[/tex].

Since [tex]x=8+3y[/tex], you can substitute this into the second equation to get

[tex](8+3y)+y=4y+8=52\implies 4y=44\implies y=11[/tex]

Then substituting this into the original second equation gives

[tex]x+11=52\implies x=41[/tex]

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