Math / Algebra

QuestionA car is purchased for $\$ 22,000$ . After each year, the resale value decreases by $30 \%$ . What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.

Studdy Solution

STEP 1

What is this asking? If a car loses 30% of its value every year, and it starts at $\$22,000$ , how much will it be worth after 3 years? Watch out! Don't forget that the car loses 30% of its current value each year, not 30% of the original value!

STEP 2

1. Calculate the value after 1 year.
2. Calculate the value after 2 years.
3. Calculate the value after 3 years.

STEP 3

Alright, so the car starts at $\$22,000$ , and it loses 30% of its value.
That means it keeps 70% of its value, right?
Because $100\% - 30\% = 70\%$ .

STEP 4

So, after 1 year, the car is worth $0.70 \cdot \$22,000$ .
Let's calculate that: $0.70 \cdot \$22,000 = \$15,400$

STEP 5

Now, we do the same thing again!
The car is worth $\$15,400$ , and it loses another 30% of that value.
So it keeps 70% of $\$15,400$ .

STEP 6

After 2 years, the car is worth $0.70 \cdot \$15,400$ .
Let's calculate that: $0.70 \cdot \$15,400 = \$10,780$

STEP 7

One more time!
The car is now worth $\$10,780$ , and it loses another 30%, keeping 70%.

STEP 8

After 3 years, the car is worth $0.70 \cdot \$10,780$ .
Let's calculate that: $0.70 \cdot \$10,780 = \$7,546$

STEP 9

After 3 years, the car will be worth approximately $\$7,546$ .

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QuestionA car is purchased for $\$ 22,000$ . After each year, the resale value decreases by $30 \%$ . What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.

Studdy Solution

STEP 1

What is this asking? If a car loses 30% of its value every year, and it starts at $\$22,000$ , how much will it be worth after 3 years? Watch out! Don't forget that the car loses 30% of its current value each year, not 30% of the original value!

STEP 2

1. Calculate the value after 1 year.
2. Calculate the value after 2 years.
3. Calculate the value after 3 years.

STEP 3

Alright, so the car starts at $\$22,000$ , and it loses 30% of its value.
That means it keeps 70% of its value, right?
Because $100\% - 30\% = 70\%$ .

STEP 4

So, after 1 year, the car is worth $0.70 \cdot \$22,000$ .
Let's calculate that: $0.70 \cdot \$22,000 = \$15,400$

STEP 5

Now, we do the same thing again!
The car is worth $\$15,400$ , and it loses another 30% of that value.
So it keeps 70% of $\$15,400$ .

STEP 6

After 2 years, the car is worth $0.70 \cdot \$15,400$ .
Let's calculate that: $0.70 \cdot \$15,400 = \$10,780$

STEP 7

One more time!
The car is now worth $\$10,780$ , and it loses another 30%, keeping 70%.

STEP 8

After 3 years, the car is worth $0.70 \cdot \$10,780$ .
Let's calculate that: $0.70 \cdot \$10,780 = \$7,546$

STEP 9

After 3 years, the car will be worth approximately $\$7,546$ .

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QuestionA car is purchased for $22,000\$ 22,000$22,000. After each year, the resale value decreases by 30%30 \%30%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.

Studdy Solution

STEP 1

What is this asking? If a car loses 30% of its value every year, and it starts at $22,000\$22,000$22,000, how much will it be worth after 3 years? Watch out! Don't forget that the car loses 30% of its *current* value each year, not 30% of the *original* value!

STEP 2

1. Calculate the value after 1 year.2. Calculate the value after 2 years.3. Calculate the value after 3 years.

STEP 3

Alright, so the car starts at $22,000\$22,000$22,000, and it loses 30% of its value.That means it *keeps* 70% of its value, right?Because 100%−30%=70%100\% - 30\% = 70\%100%−30%=70%.

STEP 4

So, after 1 year, the car is worth 0.70⋅$22,0000.70 \cdot \$22,0000.70⋅$22,000.Let's **calculate that**: 0.70⋅$22,000=$15,4000.70 \cdot \$22,000 = \$15,4000.70⋅$22,000=$15,400

STEP 5

Now, we do the same thing again!The car is worth $15,400\$15,400$15,400, and it loses another 30% of *that* value.So it keeps 70% of $15,400\$15,400$15,400.

STEP 6

After 2 years, the car is worth 0.70⋅$15,4000.70 \cdot \$15,4000.70⋅$15,400.Let's **calculate that**: 0.70⋅$15,400=$10,7800.70 \cdot \$15,400 = \$10,7800.70⋅$15,400=$10,780

STEP 7

One more time!The car is now worth $10,780\$10,780$10,780, and it loses another 30%, keeping 70%.

STEP 8

After 3 years, the car is worth 0.70⋅$10,7800.70 \cdot \$10,7800.70⋅$10,780.Let's **calculate that**: 0.70⋅$10,780=$7,5460.70 \cdot \$10,780 = \$7,5460.70⋅$10,780=$7,546

STEP 9

After 3 years, the car will be worth approximately $7,546\$7,546$7,546.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA car is purchased for $\$ 22,000$ . After each year, the resale value decreases by $30 \%$ . What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.

What is this asking? If a car loses 30% of its value every year, and it starts at $\$22,000$ , how much will it be worth after 3 years? Watch out! Don't forget that the car loses 30% of its current value each year, not 30% of the original value!

1. Calculate the value after 1 year.
2. Calculate the value after 2 years.
3. Calculate the value after 3 years.

Alright, so the car starts at $\$22,000$ , and it loses 30% of its value.
That means it keeps 70% of its value, right?
Because $100\% - 30\% = 70\%$ .

So, after 1 year, the car is worth $0.70 \cdot \$22,000$ .
Let's calculate that: $0.70 \cdot \$22,000 = \$15,400$

Now, we do the same thing again!
The car is worth $\$15,400$ , and it loses another 30% of that value.
So it keeps 70% of $\$15,400$ .

After 2 years, the car is worth $0.70 \cdot \$15,400$ .
Let's calculate that: $0.70 \cdot \$15,400 = \$10,780$

One more time!
The car is now worth $\$10,780$ , and it loses another 30%, keeping 70%.

After 3 years, the car is worth $0.70 \cdot \$10,780$ .
Let's calculate that: $0.70 \cdot \$10,780 = \$7,546$

After 3 years, the car will be worth approximately $\$7,546$ .