Question

The larger of two numbers is 5 more than the smaller. If 4 times the smaller is subtracted by 3 times the larger, the result is 29.

Find the two numbers.

Answer 1

The smaller number is 44 and the larger number is 49, derived from setting up and solving an equation based on the given conditions in the problem.

Step-by-step explanation:

Step-by-Step Solution to Find Two Numbers

Let's denote the smaller number as s. According to the problem, the larger number is 5 more than the smaller, so we can write it as s + 5. Now, we're given that 4 times the smaller number (4s) subtracted by 3 times the larger number (3(s + 5)) equals 29. To find the two numbers, we'll set up an equation and solve for s:

• 
  
• 4s - 3(s + 5) = 29
• 
  
• 4s - 3s - 15 = 29
• 
  
• s - 15 = 29
• 
  
• s = 29 + 15
• 
  
• s = 44

Now that we have the smaller number, s = 44, we can find the larger number:
s + 5 = 44 + 5 = 49.

The two numbers are 44 and 49.