Question

1. you want to buy a bicycle with your friend. you have $43.50 saved and plan to save an additional $7.25 every week. your friend has $24.50 saved and plans to save an additional $8.75 every week.

part a simplify and interpret an expression that represents the amount of money you and your friend save after w weeks.
part b after 10 weeks, you and your friend use all of the money and buy the bike. how much does the bike cost? who pays more towards the cost of the bike? explain your reasoning.

Explanation:

Part A

Step1: Define savings for each person

Your savings after \( w \) weeks: \( 43.50 + 7.25w \)
Friend's savings after \( w \) weeks: \( 24.50 + 8.75w \)

Step2: Total savings expression

Add both expressions:
\( (43.50 + 7.25w) + (24.50 + 8.75w) \)

Step3: Simplify

Combine like terms:
\( (43.50 + 24.50) + (7.25w + 8.75w) = 68 + 16w \)

Step4: Interpret

\( 68 \) is the total initial savings (\( 43.50 + 24.50 \)), and \( 16w \) is total weekly savings (\( 7.25w + 8.75w \)). The expression \( 68 + 16w \) represents total money saved by you and your friend after \( w \) weeks.

Step1: Calculate total savings at \( w = 10 \)

Use \( 68 + 16w \). Substitute \( w = 10 \):
\( 68 + 16(10) = 68 + 160 = 228 \)

Step2: Calculate your contribution

Your savings: \( 43.50 + 7.25(10) = 43.50 + 72.50 = 116 \)

Step3: Calculate friend's contribution

Friend's savings: \( 24.50 + 8.75(10) = 24.50 + 87.50 = 111.50 \)

Step4: Compare contributions

\( 116 > 111.50 \), so you pay more.

Answer:

Simplified expression is \( 68 + 16w \). It means total initial savings (\$68) plus total weekly savings (\$16 per week) after \( w \) weeks.

Part B