QuestionA house increased by $29\%$ to a current value of \$129,000. What was its original purchase value?

Studdy Solution

STEP 1

Assumptions1. The current value of the house is $129,000. The house has increased in value by29%
3. The increase in value is calculated as a percentage of the original value

STEP 2

First, we need to understand that the current value of the house is129% of the original value. This is because the house has increased in value by29%, so the current value is the original value plus29% of the original value.
$Current\, value = Original\, value + Original\, value \\times Increase\, percentage$

STEP 3

We can simplify the above equation by factoring out the original value.
$Current\, value = Original\, value \\times (1 + Increase\, percentage)$

STEP 4

Now, we can rewrite the equation to solve for the original value.
$Original\, value = Current\, value / (1 + Increase\, percentage)$

STEP 5

Now, plug in the given values for the current value and increase percentage to calculate the original value.
$Original\, value = \$129,000 / (1 +29\%)$

STEP 6

Convert the percentage to a decimal value.
$29\% =0.29$ $Original\, value = \$129,000 / (1 +0.29)$

STEP 7

Calculate the denominator.
$1 +0.29 =1.29$ $Original\, value = \$129,000 /1.29$

STEP 8

Calculate the original value.
$Original\, value = \$129,000 /1.29 = \$100,000$ The original value of the house when it was purchased was $100,000.

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