Chapter 6.4, Problem 19PPS

To determine

To determine the numbers which satisfy the given situation

Answer to Problem 19PPS

The two numbers are 3 and 9.

Explanation of Solution

Given:

Four times a number minus 5 times another number is equal to 21.

And, three times the sum of two numbers is 36.

Calculation:

Let, the two numbers be x and y .

Four times a number minus 5 times another number is equal to 21, which means,

$4x-5y=21$

And, three times the sum of two numbers is 36 , which means,

$3(x+y)=36$

Let,

$4x-5y=\mathrm{21.......}(i)$

$3(x+y)=\mathrm{36.......}(ii)$

Now, add $5\times$ equation ( ii ) and $3\times$ equation ( i ),

$\begin{array}{l}\Rightarrow 3\times (4x-5y)+5\times (3x+3y)=3\times 21+5\times 36\\ \Rightarrow 12x-15y+15x+15y=243\\ \Rightarrow 27x=243\\ \Rightarrow x=9\end{array}$

Now, substitute the value of x in equation ( i ),

$\begin{array}{l}\Rightarrow 4\times 9-5y=21\\ \Rightarrow y=3\end{array}$

Conclusion:

Therefore, the required numbers are 3 and 9.