The image shows a math problem related to a savings account scenario where a student is saving money weekly. The problem has several parts:

1. Initial Information:

   • The student has $475 in a savings account.
   • She deposits $125 into the account every week.
   • Her goal is to save $7,000 for college.

2. Questions:

   • (a) How much will be in the account after 3 weeks?
   • (b) How long will it take before she has $1,350?
   • (c) Write an equation representing the relationship between the dollar amount in her account and the number of weeks of saving.
   • (d) Graph the equation and mark the points from part A and B on your graph.

Solutions:

1. (a) Amount after 3 weeks:

   • The amount deposited each week: $125
   • Total amount after 3 weeks: $\text{Amount after 3 weeks} = 475 + (125 \times 3) = 475 + 375 = 850 \text{ dollars}$ However, the handwritten answer states $975, suggesting an initial error. Correcting this: $\text{Correct amount after 3 weeks} = 475 + (125 \times 3) = 475 + 375 = 850 \text{ dollars}$

2. (b) Time to reach $1,350:

   • Let the number of weeks be $w$.
   • The equation: $475 + 125w = 1350$
   • Solving for $w$: $125w = 1350 - 475 = 875$ $w = \frac{875}{125} = 7 \text{ weeks}$ The handwritten answer suggests it takes 6 weeks, which is incorrect based on the math. The correct time is 7 weeks.

3. (c) Equation:

   • Let $w$ be the number of weeks, and $A(w)$ be the amount in the account after $w$ weeks: $A(w) = 475 + 125w$

4. (d) Graphing:

   • On a graph, the x-axis represents the number of weeks $w$, and the y-axis represents the amount $A(w)$.
   • Plot the points (3, 850) from part (a) and (7, 1350) from part (b).
   • The graph would be a straight line with a slope of 125, starting from $475.

Would you like more details or have any questions?

Related Questions:

1. What would be the amount after 10 weeks?
2. How many weeks would it take to reach exactly $5,000?
3. If the student started with $0, how many weeks would it take to reach $7,000?
4. How would the equation change if the weekly deposit was increased to $150?
5. What is the significance of the slope in the context of this problem?

Tip:

Always recheck your calculations, especially when dealing with word problems, to ensure there are no simple arithmetic mistakes.