Math Snap

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.
$$Percentage\, increase\, as\, a\, decimal = \frac{Percentage\, increase}{100}$$

STEP 3

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

STEP 4

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

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.
$$\prod =1 + Percentage\, increase\, as\, a\, decimal$$

STEP 6

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

STEP 7

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

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 $\prod$.
$$New\, value = \prod \times Old\, value$$

STEP 9

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

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