Chapter 6.4, Problem 16P

Reasoning One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by two times the second, the result is 11. What are both numbers?

To determine

To find: The two numbers.

Answer to Problem 16P

The numbers are 8 and 4.

Explanation of Solution

Given information: One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by two times the second, the result is 11. Calculation: Let the second number be x.

Then, the first number is $3x-4$ .

According to the problem,

  $\begin{array}{l}3+2(3x-4)-2x=11\\ \Rightarrow 3+6x-8-2x=11\\ \Rightarrow 6x-2x+3-8=11\\ \Rightarrow 4x-5=11\\ \Rightarrow 4x=11+5\\ \Rightarrow 4x=16\\ \Rightarrow x=4\end{array}$

  $\therefore$ The second number $=4$

  $\therefore$ The first number $=3x-4=3\cdot 4-4=8$

Thus, the numbers are 8 and 4.