A person has (9ab + 5bc + 3ac) rupees, out of these he spends at different times (2ab + bc), ( 3/2 ac - 3/2 bc), (ab + 3bc - 2ac ) and (ab + 1/2bc + 2ac) rupees. How many rupees does he have now ?
Answers
Answer:
A person has (9ab + 5bc + 3ac) rupees, out of these he spends at different times (2ab + bc), ( 3/2 ac - 3/2 bc), (ab + 3bc - 2ac ) and (ab + 1/2bc + 2ac) rupees. How many rupees does he have now ?
Rupees he have now is 5ab + 2bc + (3/2)ac
Given:
- A person has (9ab + 5bc + 3ac) rupees,
- He spends at different times (2ab + bc), ( 3/2 ac - 3/2 bc), (ab + 3bc - 2ac ) and (ab + 1/2bc + 2ac) rupees.
To Find:
- How many rupees does he have now ?
Solution:
Like terms are the terms whose variables and their exponents are the same.
When there is a - in front of an expression in parentheses, change the sign of each term in the expression
Step 1:
Add all the spends to find total spend
Total Spend = (2ab + bc) + ( (3/2) ac - (3/2) bc) + (ab + 3bc - 2ac ) + (ab + (1/2)bc + 2ac)
Step 2:
Remove unnecessary parenthesis
2ab + bc + (3/2) ac - (3/2) bc + ab + 3bc - 2ac + ab + (1/2)bc + 2ac
Step 3:
Combine like Terms and simplify
2ab + ab + ab + bc - (3/2) bc + 3bc + (1/2)bc + (3/2) ac - 2ac + 2ac
= 4ab + 3bc + (3/2) ac
Step 4:
Subtract total spends from Money he has
(9ab + 5bc + 3ac) - ( 4ab + 3bc + (3/2) ac )
9ab + 5bc + 3ac - 4ab - 3bc - (3/2)ac
= 9ab - 4ab + 5bc - 3bc + 3ac - (3/2)ac
= 5ab + 2bc + (3/2)ac
Rupees he have now is 5ab + 2bc + (3/2)ac