# The larger of two numbers is 23. If 3 times the larger is 5 more than 8 times the smaller, find...

## Question:

The larger of two numbers is {eq}23 {/eq}.

If {eq}3 {/eq} times the larger is {eq}5 {/eq} more than {eq}8 {/eq} times the smaller, find the smaller number.

## Application of Linear Equations:

The above problem can be solved by assuming the smaller number to be 'x'. Now using the information given in the problem statement, a linear equation can be made and is solved for 'x'. The steps for calculating the value of 'x' is shown in the solution below.

## Answer and Explanation:

{eq}\text{Let the smaller number be'x'.}\\ \text{The larger number is 23.}\\ \text{It is given that 3 times the larger is 5 more than 8 times the smaller number,}\\ \therefore 3 \times 23\;=\;5+8\times x\\ \Rightarrow 69=5+8x\\ \Rightarrow 8x=64\\ \Rightarrow x=8 \\ \therefore \text{The smaller number is 8.} {/eq}

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