Math  /  Algebra

QuestionA house was valued at $302,000\$ 302,000. Over several years, the value decreased by 17%17 \%, giving the house a new value. (a) Fill in the blank to write the new value in terms of the old value.
Write your answer as a decimal. New value == \square × Old value (b) Use your answer in part (a) to determine the new value.
New value: $\$ \square

Studdy Solution

STEP 1

What is this asking? We need to figure out how much a house is worth now that its value has dropped by a certain percentage. Watch out! Don't accidentally add or subtract the percentage directly to the original value.
We need to calculate the change in value first!

STEP 2

1. Find the multiplier for the new value.
2. Calculate the new value of the house.

STEP 3

Alright, so the house *decreased* in value by **17%**.
This means we *lost* some of the original value.

STEP 4

To find out how much value is *left*, we need to subtract the percentage decrease from **100%**, which represents the **initial value** of the house.
Think of it like this: we start with the *whole* value (100%) and take away a piece (17%).

STEP 5

So, we have 100%17%=83%100\% - 17\% = 83\%.
This means the new value is **83%** of the old value.

STEP 6

Now, let's convert this percentage to a decimal by dividing by **100**.
So, 83%=83100=0.8383\% = \frac{83}{100} = 0.83.
This is our **multiplier**!

STEP 7

We know the **old value** of the house was $302,000\$302,000 and the **multiplier** we found is **0.83**.

STEP 8

To find the **new value**, we multiply the **old value** by the **multiplier**: New value=0.83$302,000 \text{New value} = 0.83 \cdot \$302,000

STEP 9

Let's do the math: 0.83$302,000=$250,660 0.83 \cdot \$302,000 = \$250,660

STEP 10

(a) New value =0.83×= 0.83 \times Old value (b) New value: $250,660\$250,660

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord