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One number is five more than three times another. If their sum is increased by one, the result is twenty-six. Find the numbers.The smaller of the numbers is ? and the larger is ? .

Sagot :

Let:

x = The smaller number

y = The larger number

[tex]y=3x+5_{\text{ }}(1)[/tex][tex]x+y+1=26_{\text{ }}(2)[/tex]

Replace (1) into (2):

[tex]x+3x+5+1=26[/tex]

Add like terms:

[tex]4x+6=26[/tex]

Solve for x:

[tex]\begin{gathered} 4x=26-6 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]

Replace x into (1):

[tex]\begin{gathered} y=3(5)+5 \\ y=20 \end{gathered}[/tex]

Answer:

The smaller number is 5

The larger number is 20

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