Nora's father gives her $100 as her monthly allowance.
(a) If she spends an average of $3 each day, find the amount of money she is left with after
(i) 2 days,
(ii) 5 days,
(iii) 10 days.
(b) Given that y represents the amount of money Nora has left after x days, copy and complete the table.
| x | 2 | 5 | 10 |
|---|---|---|----|
| y | | | |
(c) On a sheet of graph paper, using a scale of 2 cm to represent 5 days on the horizontal axis and 1 cm to represent $10 on the vertical axis, plot the pairs of values of (x, y).
Answer (2)
Nora spends $3 each day from her $100 allowance. After 2 days she has $94 left, after 5 days $85, and after 10 days $70. The completed table and points for graphing have been provided for visualization.
;
Calculate the amount spent after 2, 5, and 10 days.
Subtract the spent amount from the initial allowance of $100 to find the remaining amount for each case.
Complete the table with the calculated remaining amounts.
Plot the points (2, 94), (5, 85), and (10, 70) on a graph with the specified scale.
Explanation
Problem Analysis Nora starts with $100 and spends $3 each day. We need to calculate how much money she has left after 2, 5, and 10 days. Then, we'll complete the table and plot the points on a graph.
Calculating Remaining Amount After 2 Days After 2 days, Nora spends $2 \times 3 = $6. So, she has $100 - 6 = $94 left.
Calculating Remaining Amount After 5 Days After 5 days, Nora spends $5 \times 3 = $15. So, she has $100 - 15 = $85 left.
Calculating Remaining Amount After 10 Days After 10 days, Nora spends $10 \times 3 = $30. So, she has $100 - 30 = $70 left.
Completing the Table Now, we complete the table with the calculated values:
x
2
5
10
y
94
85
70
Plotting the Points on a Graph Finally, we plot the points (2, 94), (5, 85), and (10, 70) on a graph. The horizontal axis represents the number of days (x), and the vertical axis represents the amount of money left (y). The scale is 2 cm to represent 5 days on the horizontal axis and 1 cm to represent $10 on the vertical axis.
Examples
Understanding how money decreases over time with consistent spending is crucial for budgeting. For example, if you earn a fixed amount each month and spend a certain amount daily, you can use this math to predict how much money you'll have left at the end of the month. This helps in planning expenses and saving money effectively. For instance, if you start with $500 and spend $15 a day, after 10 days you'll have $500 - (10 \times 15) = $350.
