# The sum of two numbers is 56. The larger number is 7 less than 3 times the smaller number. Find...

## Question:

The sum of two numbers is {eq}56 {/eq}. The larger number is {eq}7 {/eq} less than {eq}3 {/eq} times the smaller number.

Find the smaller number.

## System of equation:

A system of linear equations is used to determine the values of the variables. If the number of equations is equal to the number of the variables, then the system of equation is deterministic; otherwise, the system of equations is indeterministic.

## Answer and Explanation:

Suppose that the numbers are p and q

Write the expression according to the question.

{eq}\begin{align*} p + q &= 56.... ........(I)\\ p &= 3q - 7..............(II) \end{align*} {/eq}

Substitute {eq}3q - 7 {/eq} for {eq}p {/eq} in equation (I).

{eq}\begin{align*} 3q - 7 + q &= 56\\ 4q &= 56 + 7\\ 4q &= 63\\ q &= 15.75 \end{align*} {/eq}

Thus, the smaller number is {eq}15.75 {/eq}.

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from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 9