Linear Equations and Inequalities
Finding the multiplier to give a final amount after a percentage increase ...

A house was valued at $\$ 261,000$. Over several years, the value decreased by $8 \%$, 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 $=\square \times$ Old value
(b) Use your answer in part (a) to determine the new value.
New value: $s \square$

Step 1 ：Given that the house was initially valued at $261,000 and the value decreased by 8%, we need to find the new value of the house.

Step 2 ：To find the new value, we subtract the percentage decrease from 100% (or 1 in decimal form) and then multiply the result by the old value. This gives us the formula: New value = (1 - 0.08) * Old value.

Step 3 ：Substituting the given values into the formula, we get: New value = 0.92 * $261,000.

Step 4 ：Calculating the above expression, we find that the new value of the house is $240,120.

Step 5 ：Thus, the multiplier to give the new value after an 8% decrease is 0.92 and the new value of the house is $240,120.