Question

Two sisters, Jenny and Jada, are saving money for summer vacation. Their mom gets them started by giving the two sisters, Jenny and Jada, $25. Each sister will put part of the pay from their after-school job in the account each week. Jenny will deposit $8 per week. Jada will each deposit $5 per week.

1. Make a table for the total savings for each sister.
2. Graph each sister’s savings on the same set of axes.
3. Find the slope and y-intercept of the graph of each sister.
4. Model each sister’s savings plan using an equation in the form y = mx + b.
5. How much will each sister have after 3 weeks? After 7 weeks?

6. Who will have more money saved? Explain how you know?

Answer 1

Explanation:

This problem requires the use of the Pythagorean Theorem to find the lengths of the sides of a piece of property in the shape of a right triangle

Example:

Taylor finds a piece of property in the shape of a right triangle. She finds that the longer leg is 10 m shorter than twice the length of the shorter leg and the hypotenuse is 20 m longer than the longer leg. Find the lengths of the sides of the triangular lot.

Answer 2

The details of the amount saved weekly indicates;

1.

`\begin{tabular} \cline{1-3}Week & Amount Saved by Jenny (\$)& Amount Saved by Jada (\$)\\ \cline{1-3}0 &25&25 \\\cline{1-3}1 &33 & 30\\\cline{1-3}2 & 41 &35 \\\cline{1-3}3 &49&40 \\\cline{1-3}4 & 57 & 45 \\\cline{1-3}5 &65&50 \\\cline{1-3}\end{tabular}`

2. Please find attached the graph of each sister's savings, created with MS Excel

3. Slope and y-intercept for Jada are $8, and $25 respectively

Slope and y-intercept for Jane are $5 and $25 respectively

4. Equation for Jenny is; y = 8·x + 25

Equation for Jada is; y = 5·x + 25

5. Amount in the savings after 3 weeks

Jenny; $49

Jada:$40

Amount saved after 7 weeks

Jenny; $81

Jada; $60

6. Jenny

The steps used to find the above values are presented as follows;

The amount Jenny and Jada's starts their savings with = $25 given to them by their mom

The amount Jenny deposits each week = $8

Amount Jada deposits each week = $5

The total savings for each sister can be presented in a the following tabular form;

Week Jenny Jada

0 $25 $25

1 $33 $30

2 $41 $35

3 $49 $40

4 $57 $45

5 $65 $50

2. The above values can be used to graph each sister's savings. Please find the graph of the savings by Jenny and Jada on the same axis, created with MS Excel

3. The slope of the graph for the savings is the rate at which the y-value increases per unit increase in the x-value, which is the amount each sister earns weekly from their after school jobs, therefore;

The slope for Jenny's graph = 8

The slope for Jada's graph = 5

The y-intercept is the point on the graph where the graph intersects the y-axis, which corresponds to where the x-value is zero, which is the starting point on the graphs based on natural numbers.

The starting values for Jenny and Jada are both (0, 25), which indicates that the y-value of the y-intercept of the graph Jenny and Jada is y = 25

4. The equation y = mx + b is the slope-intercept form of the equation for a line, where m is the slope and b is the y-value of the y-intercept

The equation for the saving plan for Jenny is; y = 8·x + 25

The equation for the saving plan for Jada is; y = 5·x + 25

5. The amount each sister has after 3 weeks are;

Amount Jenny has; 8 × 3 + 25 = $49

Amount Jada has; 5 × 3 + 25 = $40

The amount each sister have after 7 weeks are

Jenny; 8 × 7 + 25 = $81

Jada; 5 × 7 + 25 = $60

6. The rate at which Jenny saves is higher than the rate Jada is saving, therefore Jenny saves more money