A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month.
(amounts_from_second_month) ₹800, ₹950, ₹1100
(linear_expression) 500 + 150n
Explanation
The student starts with an initial amount of ₹500 and adds ₹150 every month. At the end of the first month, she has ₹650. From the second month onwards, the amounts are ₹800, ₹950, etc. Following the pattern of linear expressions shown in the textbook examples (like 200 + 50m for the chess club), the amount for the nth month is formulated by adding the monthly pocket money multiplied by the number of months to the initial amount.
Solution Steps
Step 1: Identify the initial amount and the constant monthly increase. The student has an initial amount of ₹500 in her savings account and gets ₹150 every month as pocket money.
Step 2: Calculate the amount at the end of each month. At the end of the first month, she will have 500 + = ₹650. At the end of the second month, she will have 500 + = ₹800. At the end of the third month, she will have 500 + = ₹950.
Step 3: State the money she will have from the second month onwards. The amounts will be ₹800, ₹950, ₹1100, and so on.
Step 4: Formulate the linear expression for the nth month. Since the amount increases by a constant value of ₹150 each month, the linear expression to represent the amount she will have in the nth month is 500 + 150n.