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QuestionA house valued at \$263,000 increased by 15%.
(a) New value = ∏× \prod \times Old value.
(b) Find the new value. New value: \$ \square

Studdy Solution

STEP 1

Assumptions1. The initial value of the house is $263,000. The value of the house increased by15%
3. The increase is calculated as a one-time increase, not compounding annually

STEP 2

First, we need to express the percentage increase as a decimal. This can be done by dividing the percentage by100.
Percentage increase as a decimal=Percentage increase100Percentage\, increase\, as\, a\, decimal = \frac{Percentage\, increase}{100}

STEP 3

Now, plug in the given value for the percentage increase to calculate the decimal.
Percentage increase as a decimal=15100Percentage\, increase\, as\, a\, decimal = \frac{15}{100}

STEP 4

Calculate the decimal value of the percentage increase.
Percentage increase as a decimal=15100=0.15Percentage\, increase\, as\, a\, decimal = \frac{15}{100} =0.15

STEP 5

To find the new value, we need to add the original value to the increase. This can be expressed as a multiplication of the original value by1 plus the decimal value of the percentage increase.
∏=1+Percentage increase as a decimal\prod =1 + Percentage\, increase\, as\, a\, decimal

STEP 6

Plug in the value for the percentage increase as a decimal to calculate the value of ∏\prod.
∏=1+0.15\prod =1 +0.15

STEP 7

Calculate the value of ∏\prod.
∏=1+0.15=1.15\prod =1 +0.15 =1.15

STEP 8

Now that we have the value of ∏\prod, we can find the new value of the house by multiplying the old value by ∏\prod.
New value=∏×Old valueNew\, value = \prod \times Old\, value

STEP 9

Plug in the values for ∏\prod and the old value to calculate the new value.
New value=.15×$263,000New\, value =.15 \times \$263,000

STEP 10

Calculate the new value of the house.
New value=.15×$263,000=$302,450New\, value =.15 \times \$263,000 = \$302,450The new value of the house is $302,450.

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