A $200 bike goes down 10%, then down 10%. What is the new price? Step by Step

Step by step

The question

Question: A $200 bike goes down 10%, then down 10%.

What is the new price?

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Down 10% of $200

Percent means out of 100.

So 10% is 10 out of 100.

That is the same as 1 out of 10: one tenth.

$200 divided by 10 is $20.

10% of $200 = $200 ÷ 10 = $20

To find 10%, we divide by 10.

10% = ÷ 10

Down 10% means we take away $20.

$200 minus $20 is $180.

new price = $200 − $20 = $180

2 Down 10% of $180

Now the price is $180.

The second 10% is not of the old number.

It is 10% of the new number, $180.

To find 10%, we divide by 10.

$180 divided by 10 is $18.

10% of $180 = $180 ÷ 10 = $18

Down 10% means we take away $18.

$180 minus $18 is $162.

new price = $180 − $18 = $162

Careful!

We can't just add the percents.

The second percent is of a new number.

Careful: not −10% − 10% = −20%: $160 ✗

So the new price is $162.

3 Check

Let's check another way: down 10% leaves 100% minus 10%.

That is 90% of the price.

90% is 90 out of 100: 0.9.

$200 times 0.9 is $180.

100% − 10% = 90% = 0.9: $200 × 0.9 = $180

Then: down 10% leaves 100% minus 10%.

That is 90% of the price.

90% is 90 out of 100: 0.9.

$180 times 0.9 is $162.

The same.

So the answer is right!

100% − 10% = 90% = 0.9: $180 × 0.9 = $162

4 Pick the choice

Our answer is $162.

That is choice C.

C) $162

5 Why not the others

A is $38.

Wrong: that is the money taken off: 20 + 18.

A) $38 ✗ that is the money taken off: 20 + 18

B is $160.

Wrong: 20% off at once: the second 10% is of $180.

That is the Careful mistake from before.

B) $160 ✗ 20% off at once: the second 10% is of $180

D is $180.

Wrong: that is the price after the first change only.

D) $180 ✗ that is the price after the first change only

Let's look back.

First: down 10% of $200.

Then: down 10% of $180.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer