Question

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 ? .

Answer 1

Let:

x = The smaller number

y = The larger number

$y=3x+5_{\text{ }}(1)$$x+y+1=26_{\text{ }}(2)$

Replace (1) into (2):

$x+3x+5+1=26$

Add like terms:

$4x+6=26$

Solve for x:

$\begin{gathered} 4x=26-6 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}$

Replace x into (1):

$\begin{gathered} y=3(5)+5 \\ y=20 \end{gathered}$

Answer:

The smaller number is 5

The larger number is 20