The World of Numbers | Exercise 3.2

Question 2

A spice trader takes a loan (debt) of ₹850. The next day, he makes a profit (fortune) of ₹1,200. The following week, he incurs a loss of ₹450. Write this sequence as an equation using integers and calculate his final financial standing.

Solution

Understand the Question

Represent the transactions using positive and negative integers:
- Loan/Debt: Money owed, represented as a negative integer ( $-850$ ).
- Profit/Fortune: Money gained, represented as a positive integer ( $+1200$ ).
- Loss: Money lost, represented as a negative integer ( $-450$ ).
To find the final financial standing, sum all the integer values together.

Step 1 · Form the Equation

Representing the transactions with integers:

Debt of ₹850 $= -850$
Profit of ₹1,200 $= +1200$
Loss of ₹450 $= -450$

Equation representing the sequence: $-850 + 1200 - 450$

Step 2 · Calculate the Final Financial Standing

Adding the integers from left to right:

\begin{aligned} -850 + 1200 - 450 &= 350 - 450 \\ &= -100 \end{aligned}

Answer

Equation: $-850 + 1200 - 450$ Final financial standing: $-\text{₹}100$ (a net loss of $\text{₹}100$ )

Common Mistakes

Incorrect Sign Conventions: Treating debt or loss as positive values instead of negative integers.
Sign Errors in Arithmetic: Making errors when combining positive and negative integers (e.g., computing $-850 + 1200$ as $-350$ instead of $+350$ ).

Question 2

More questions in Exercise 3.2