Question

A house was valued at $329,000. Over several years, the value decreased by 16%, giving the house 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 = _ x Old value
(b) Use your answer in part (a) to determine the value.
New value: $_

Answer 1

(a) New value = .84 × Old value

(b) New value: $329,000(.84^t)

Answer 2

a)
`\sf x =\underline{\;\; 0.84 \;\;}* y`

b)
`\sf \textsf{New value} = \underline{\;\; \$276,360\;\;}`

Explanation:

Part (a)

To find the new value in terms of the old value when the value decreases by 16%, we multiply the old value by
`\sf 1 - \textsf{percentage decrease}`.

Let
`\sf x` be the new value, and
`\sf y` be the old value.

`\sf x = (1 - \textsf{percentage decrease}) * y`

In this case, the percentage decrease is 16%(0.16 in decimal), so:

`\sf x = (1 - 0.16) * y`

`\sf x = 0.84 * y`

So, the new value is 0.84 times the old value.

Part (b)

Now, substitute the given old value ($329,000) into the expression we found in part (a):

`\sf \textsf{New value} = 0.84 * \textsf{Old value}`

`\sf \textsf{New value} = 0.84 * \$329,000`

`\sf \textsf{New value} = \$276,360`

Therefore, the new value of the house is $276,360 after a 16% decrease in value.