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I'm not exactly sure how to do this. I know the answer is $£64,000$ but whatever I try, nothing is working.

i.e. $£80,000$ x $25%$ $= 2,000,000$ devided by $100$ $=$ $20,000$

$£80,000 - £20,000 = £60,000$

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Let's call $x$ the value of the houses one year ago. So you have:

$$1.25 \cdot x = 80.000$$

Because the value of the houses now is a $25\%$ increase over the value of the houses one year ago ($x$).

Solving for $x$ gives you the correct value.

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Recall that $25\% = \dfrac{25}{100} = 0.25$.

So we have some amount, $x$, that when increased by $25\%$ is equal to $80,000$.

Translating into math: $$x + 0.25 \times x = 80,000 \iff 1.25 x = 80,000 \iff x = \dfrac{80,000}{1.25} = 64000$$

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This is saying for a number $x$, if it increased by 25%, then it totals to $$\$80,000$$

So we can say that:

$$x + 0.25x = \$80000$$ $$1.25x = \$80000$$ $$x= \$64000$$

So your answer is $\$64000$.

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Just to add to Varun

$$x+0.25x=80000,$$

which is the same as saying $1.25x = 8000$, therefore

$$x = \frac{80000}{1.25} = 64000.$$

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What you're asking is this:

125% of what is 80,000?

Algebraically:

  1. 1.25x = 80,000
  2. Divide both sides by 1.25:
    12.5x/1.25 = 80,000/1.25
  3. Simplify: x = 64,000

x = 64,000 is the answer you're looking for, i.e., the price of the house a year ago.

Check to see that that is right:

Calculate a 25% increase on 64,000:
25% x 64,000 =16,000
Add that increase to last year's price:
64,000 + 16,000 = 80,000
80,000 is this year's price, so it looks good.

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