Question

the balance of sams account, y, based on the number of weeks spent saving, x, can be represented by $y = 35x + 10$. the balance of his sisters account based on the weeks spent saving is shown on the graph.

statement | t/f?
sam is saving more money per week than his sister. |
sam started with less money in his account than his sister. |
after 5 weeks, sams sister will have $25 less in her account than sam. |

rewrite the false statement to make it true:

Explanation:

Step1: Find Sam's savings parameters

Sam's savings: $y = 35x + 10$.

• Weekly savings (slope): $35$
• Initial amount (y-intercept): $10$

Step2: Find sister's savings parameters

From the graph:

• When $x=0$, $y=60$ (initial amount)
• When $x=5$, $y=190$. Weekly savings: $\frac{190-60}{5}=26$

Sister's equation: $y=26x+60$

Step3: Test first statement

Compare weekly savings: $35>26$
Sam saves more per week.

Step4: Test second statement

Compare initial amounts: $10<60$
Sam started with less.

Step5: Test third statement

Sam at 5 weeks: $y=35(5)+10=185$
Sister at 5 weeks: $y=26(5)+60=190$
Difference: $190-185=5$. Sister has $5$ more, not $25$ less.

Step6: Rewrite false statement

Adjust the incorrect claim to match the calculation.

Answer:

1. Sam is saving more money per week than his sister.: True
2. Sam started with less money in his account than his sister.: True
3. After 5 weeks, Sam's sister will have $25 less in her account than Sam.: False

Rewritten true statement: After 5 weeks, Sam's sister will have $5 more in her account than Sam.