Question

saving money
everyday on her way home from school, jen uses $1 to buy a bag of chips. the chips cost $0.75, and she saves the remaining quarter in her change jar.
a. jen buys 5 bags of chips per week. at this rate, how long will it take her to save $10.00?

b. write an equation to show how much money, y, jen will save after any number of weeks, x.

c. create a graph to represent this relationship.

mark is also trying to save money. he already has $3.00 saved and puts $1.00 per week away in his piggy bank. this can be represented by the equation $y = x + 3$.

d. will jen or mark save $20.00 first? justify your reasoning.

e. imagine you have made a graph to represent the money mark has saved. explain why mark’s line does not start at the origin and jen’s line does start at the origin.

Explanation:

Part a

Step1: Find weekly savings

Each bag saves $0.25, 5 bags: $0.25×5 = $1.25 per week.

Step2: Calculate time for $10

Time = Total / Weekly = 10 / 1.25 = 8 weeks.

Step1: Define variables

x = weeks, y = total savings.

Step2: Form equation

Weekly savings: $1.25, so y = 1.25x.

Step1: For Jen

Set y = 20 in \( y = 1.25x \). Solve: \( 20 = 1.25x \) → \( x = 20 / 1.25 = 16 \) weeks.

Step2: For Mark

Set y = 20 in \( y = x + 3 \). Solve: \( 20 = x + 3 \) → \( x = 17 \) weeks.

Step3: Compare

16 < 17, so Jen saves first.

Answer:

8 weeks

Part b