Question

practice it
practice writing linear equations from word problems
linear functions show up all around you, including in your bank account! practice writing linear equations for each of the banking scenarios below.

1. andre has $157 in his checking account and earns $120 per week at his part - time job. assume he has no expenses currently.

a. create a table to show his balance, y, after x weeks.
table with x and y columns
b. write an equation to show the total amount in his account, y, after x weeks.
c. how much does he have after 8 weeks?

1. valentina opens a checking account with a $12 monthly maintenance fee. she deposits $517 and makes no other deposits or withdrawals.

a. create a table to show her balance, y, after x months.
table with x and y columns
b. write an equation to show the total amount in her account, y, after x months.
c. how much does she have after 1 year?

1. jackson has $650 in their account and uses their debit card to take out $40 cash each week. their card has a $5 atm fee.

a. write an equation to express their balance, y, after x weeks.
b. what will their balance be after 8 weeks?
c. after 8 weeks, how much will jackson have paid in atm fees alone?

1. mae has $215 in her account and withdraws $120 one time. each month her balance is below $100, she pays a $7 fee.

a. write an equation to express her balance for the next x months, if she makes no deposits or withdrawals.
b. what will her balance be after 3 months?
c. challenge: during which month will mae start being charged overdraft fees?

Explanation:

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Problem 1: Andre's Account

Step1: Fill table with x values

Choose x = 0,1,2,3,4

Step2: Calculate y for each x

$y = 157 + 120x$

• $x=0$: $y=157+120(0)=157$
• $x=1$: $y=157+120(1)=277$
• $x=2$: $y=157+120(2)=397$
• $x=3$: $y=157+120(3)=517$
• $x=4$: $y=157+120(4)=637$

Step3: Write linear equation

Initial amount + weekly earnings: $y=120x+157$

Step4: Compute 8-week balance

Substitute $x=8$: $y=120(8)+157$
$y=960+157=1117$

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Problem 2: Valentina's Account

Step1: Fill table with x values

Choose x = 0,1,2,3,4

Step2: Calculate y for each x

$y = 517 - 12x$

• $x=0$: $y=517-12(0)=517$
• $x=1$: $y=517-12(1)=505$
• $x=2$: $y=517-12(2)=493$
• $x=3$: $y=517-12(3)=481$
• $x=4$: $y=517-12(4)=469$

Step3: Write linear equation

Initial deposit - monthly fee: $y=-12x+517$

Step4: Compute 1-year balance

1 year = 12 months, substitute $x=12$:
$y=517-12(12)=517-144=373$

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Problem 3: Jackson's Account

Step1: Write weekly withdrawal total

Total weekly withdrawal: $40+5=45$

Step2: Write linear equation

Initial amount - weekly deductions: $y=-45x+650$

Step3: Compute 8-week balance

Substitute $x=8$:
$y=650-45(8)=650-360=290$

Step4: Calculate total ATM fees

Fees per week = $5$, 8 weeks: $5\times8=40$

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Problem 4: Mae's Account

Step1: Calculate initial post-withdrawal balance

$215-120=95$

Step2: Write linear equation

Post-withdrawal balance - monthly fees: $y=95-7x$

Step3: Compute 3-month balance

Substitute $x=3$:
$y=95-7(3)=95-21=74$

Step4: Find fee start month

Post-withdrawal balance = $95 < 100$, so fees start in Month 1

Answer:

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1. Andre's Account

a. Table:

x	y
1	277
2	397
3	517
4	637

b. $y = 120x + 157$
c. $\$1117$

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2. Valentina's Account

a. Table:

x	y
1	505
2	493
3	481
4	469

b. $y = -12x + 517$
c. $\$373$

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3. Jackson's Account

a. $y = -45x + 650$
b. $\$290$
c. $\$40$

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4. Mae's Account

a. $y = 95 - 7x$
b. $\$74$
c. Month 1