Final answer:
To solve for the two numbers, two equations are established based on the problem statement. The equations are solved for two variables representing the numbers, which results in the smaller number being 3 and the larger number being 10.
Step-by-step explanation:
The question asks to find two numbers where their difference is 7 and when three times the smaller number is taken from twice the larger number, the result is 11. Let's call the larger number x and the smaller number y. According to the problem, we have two equations:
1) x - y = 7
2) 2x - 3y = 11.
First, we solve equation 1 for x: x = y + 7. Next, we substitute x into equation 2:
2(y + 7) - 3y = 11
2y + 14 - 3y = 11
-y + 14 = 11
y = 3. Now that we have found y,
we use equation 1 to find x: x = 3 + 7 = 10. Therefore, the two numbers are 3 and 10.