Question

The sum of two numbers is 16the large numbers is four less than three times the smaller number.find the numbers

Answer 1

Given the question in the tab, the following are the solution steps to answer the question.

STEP 1: Represent the numbers

Let the larger number be represented by x

Let the smaller number be represented by y

STEP 2: Interpret the statements

Sum of the numbers equal 16

`x+y=16`

Large number is four less than three times the smaller number

`x=3y-4`

STEP 3: Solve for the numbers using substitution method

`\begin{gathered} \text{By substitution,} \\ (3y-4)+y=16 \\ 3y+y=16+4 \\ 4y=20 \\ y=(20)/(4) \\ y=5 \end{gathered}`

Solve for x using substitution.

`\begin{gathered} x+y=16 \\ x=16-y \\ By\text{ substitution,} \\ x=16-5 \\ x=11 \end{gathered}`

Hence, the numbers are 11 and 5