Question

for each scenario, write a linear equation to model whats happening, and then solve the equation to answer the question.1. melody has $50 in her savings account right now. she wants to save $250 for a taylor swift concert ticket. she figures she can save $20/week from her part-time job.a. write an equation to model her savings account balance after x weeks.b. how long will it take to be able to afford the ticket?2. after a really rough winter, kristoff cant afford to fix his sled until he has $7000 saved. every month, his take-home pay is $2500, and he uses the 50/30/20 rule to determine how much hell spend and save.a. write an equation to model kristofs savings after x months.b. how long will it be before he can get his sled fixed if hes already got $900 in the bank?3. raven is starting with absolutely no savings, but she wants to have an emergency fund of $10,000 saved by the end of her first year at her new job.a. how much will she need to save per month in order to meet this savings goal?b. what would ravens take-home pay need to be in order for that monthly savings target to represent 20% of her pay?4. fill-in-the blanks to write a word problem for your own personal savings goal.right now i have _____ already saved. this money is located in ________. i would like to have a total of ___ in order to _________________________________5. select one of these two statements to complete:□ i can save ___ per month, which means it will take me ___ to reach my goal.□ i would like to reach my goal in ___ months, so ill need to save _____ per month.

Explanation:

Step1: Define variables & base savings

Let $B$ = balance, $x$ = weeks. Initial savings: $\$50$, weekly save: $\$20$.
$B = 50 + 20x$

Step2: Set balance to target, solve for $x$

Target = $\$250$. Set $50 + 20x = 250$
$20x = 250 - 50$
$20x = 200$
$x = \frac{200}{20} = 10$

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Step1: Calculate monthly savings, write equation

50/30/20 rule: 20% for savings. Monthly pay: $\$2500$.
Monthly save = $0.20 \times 2500 = 500$. Let $S$ = savings, $x$ = months.
$S = 500x$

Step2: Add existing savings, solve for $x$

Existing savings: $\$900$, target: $\$7000$.
$900 + 500x = 7000$
$500x = 7000 - 900$
$500x = 6100$
$x = \frac{6100}{500} = 12.2$

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Step1: Divide total by 12 months

Total goal: $\$10,000$, time: 12 months.
Monthly save = $\frac{10000}{12} \approx 833.33$

Step2: Set savings = 20% of pay, solve

Let $P$ = take-home pay. $0.20P = 833.33$
$P = \frac{833.33}{0.20} = 4166.65$

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Step1: Fill in personal savings details (example)

Right now I have $\$1000$ already saved. This money is located in a high-yield savings account. I would like to have a total of $\$5000$ in order to buy a used car.

Step2: Select and complete statement (example)

$\square$ I can save $\$300$ per month, which means it will take me $13.33$ to reach my goal.

Answer:

1. a. $B = 50 + 20x$

b. 10 weeks

1. a. $S = 500x$

b. 12.2 months

1. a. $\approx\$833.33$ per month

b. $\approx\$4166.65$

1. (Example) Right now I have $\$1000$ already saved. This money is located in a high-yield savings account. I would like to have a total of $\$5000$ in order to buy a used car.
2. (Example) $\square$ I can save $\$300$ per month, which means it will take me $13.33$ to reach my goal.