Question

Sam is solving the following word problem by substitution. Identify on which line a mistake was made. One number added to three times another number is 24. Five times the first number added to three times the other number is 36. Find the numbers.

a. Line 1
b. Line 2
c. Line 3
d. Line 4

Answer 1

The mistake was made on Line 4 where the equation was written incorrectly as x = 24 - y instead of x = 24 - 3y.

Step-by-step explanation:

The mistake was made on Line 4. Let's go through the problem step by step to see where the mistake occurred:

1. 
   
3. Let the first number be x and the second number be y. We have the equation x + 3y = 24.
4. 
   
6. We are given that 5 times the first number plus 3 times the second number is 36, so we can write the equation 5x + 3y = 36.
7. 
   
9. Now we use substitution to solve the system of equations. We can rearrange the first equation to solve for x, giving us x = 24 - 3y.
10. 
    
12. The mistake occurs here, where the equation is incorrectly written as x = 24 - y. The 3y term is missing.
13. 
    
15. To correct the mistake, we should rewrite the equation x = 24 - 3y.
16. 
    
18. Substituting this correct equation into the second equation, we get 5(24 - 3y) + 3y = 36.
19. 
    
21. Simplifying, we have 120 - 15y + 3y = 36.
22. 
    
24. Combining like terms, we get -12y = -84.
25. 
    
27. Dividing both sides by -12, we find y = 7.
28. 
    
30. Finally, substituting this value of y back into the first equation, we can solve for x: x + 3(7) = 24, which gives us x = 3.

Therefore, the correct answer is that the mistake was made on Line 4.