Question

The sun of two numbers is 33. The larger number is 3 more than two times the smaller number. What are the numbers?

Answer 1

Given:

Sum of two numbers = 33

The larger number is 3 more than two times the smaller number.

Find the number

Sol:

Let a smaller number be "x"

So larger number is:

$\begin{gathered} \text{ Smaller number = }x \\ \\ \text{ larger number = }2x+3 \end{gathered}$

Sum of the two numbers is 33.

Then,

$\begin{gathered} \text{ Smaller number }+\text{ Larger number = }33 \\ \\ x+2x+3=33 \end{gathered}$

Solve for "x"

$\begin{gathered} x+2x+3=33 \\ \\ 3x+3=33 \\ \\ 3x=33-3 \\ \\ 3x=30 \\ \\ x=\frac{30}{3} \\ \\ x=10 \end{gathered}$

So, the smaller number is 10

$\begin{gathered} \text{ larger number =}2x+3 \\ \\ =2(10)+3 \\ \\ =20+3 \\ \\ =23 \end{gathered}$

The larger number is 23.

$\begin{gathered} \text{ Smaller number = }10 \\ \\ \text{ Larger number =}23 \end{gathered}$