Question

Write the following expression using the fewest possible terms. The expression quantity three fourths times t minus 5 plus two fifths times t end quantity minus quantity five eighths times t plus 17 end quantity negative 71 over 40 times t plus negative 12

a) 71/40t - 22
b) 71/40t - 12
c) 21/40t - 22
d) 21/40t - 12

Answer 1

c) 21/40t - 22. To simplify the given expression, combine like terms and perform necessary calculations. The simplified expression is (21/40)t - 22. Option (c) is correct.

Step-by-step explanation:

To simplify the expression, we need to combine like terms and perform the necessary calculations. Let's break down the expression step by step:

1. 
   
3. Three-fourths times t can be rewritten as (3/4)t.
4. 
   
6. Two-fifths times t can be written as (2/5)t.
7. 
   
9. Five-eighths times t can be written as (5/8)t.
10. 
    
12. Combining all the terms, the simplified expression becomes (3/4)t - 5 + (2/5)t - ((5/8)t + 17) - (71/40)t - 12.
13. 
    
15. Simplifying further, we have (3/4)t - 5 + (2/5)t - (5/8)t - 17 - (71/40)t - 12.
16. 
    
18. Combining the like terms, the simplified expression is (3/4 - 5/8 - 71/40)t + (2/5 - 17 - 12).
19. 
    
21. This simplifies to (21/40)t - 22.

Therefore, the expression can be written as (21/40)t - 22. Option (c) is the correct answer.