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,
(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 has $94 left after 2 days, $85 after 5 days, and $70 after 10 days. The table of values has been completed accordingly. Additionally, the points can be plotted on a graph to visualize her spending over time.
;
Calculate the amount left after 2 days: 100 − 2 × 3 = 94 .
Calculate the amount left after 5 days: 100 − 5 × 3 = 85 .
Calculate the amount left after 10 days: 100 − 10 × 3 = 70 .
Plot the points (2, 94), (5, 85), and (10, 70) on a graph. The final amounts left are 94 , 85 , 70 .
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.
Money left after 2 days After 2 days, Nora has: 100 − 2 × 3 = 100 − 6 = 94 So, she has $94 left.
Money left after 5 days After 5 days, Nora has: 100 − 5 × 3 = 100 − 15 = 85 So, she has $85 left.
Money left after 10 days After 10 days, Nora has: 100 − 10 × 3 = 100 − 30 = 70 So, she has $70 left.
Completing the table Now, let's complete the table:
x
2
5
10
y
94
85
70
Plotting the graph Finally, we need to plot the points (2, 94), (5, 85), and (10, 70) on a graph paper using the given scale. 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 x-axis and 1 cm to represent $10 on the y-axis.
Examples
Understanding how to manage an allowance and track spending is a practical skill. For example, if Nora wants to save up for a new book that costs $35 , she can use this math to figure out how many days she needs to save her money. If she saves $5 a day instead of spending it, she can calculate how long it will take to reach her goal: 35/5 = 7 days. This type of budgeting and planning is useful for managing personal finances and making informed spending decisions.
