a scooter is priced between $1000 and $2000. its price is a multiple of 10. All the digits in the price, except for the thousands digit, are even numbers. The value of the hundreds digit is 30 times the value of the tens digit. what is the price of the scooter?

between $1000 and $2000

1xxx

a multiple of 10
1xx0

hundreds digit is 30 times the value of the tens digit
1620

..40 not possible, or 30x would be too big

1,620

Let's break down the given information step by step to find the price of the scooter:

1. The price of the scooter is a multiple of 10. This means the price ends with a 0.

2. All the digits in the price, except for the thousands digit, are even numbers. The possible even digits are 0, 2, 4, 6, and 8.

3. The value of the hundreds digit is 30 times the value of the tens digit. Let's call the tens digit 'x'. Since the hundreds digit is 30 times the value of the tens digit, the hundreds digit should be 30x.

Now let's find the possible values for x:

If x = 0, the hundreds digit would be 30 × 0 = 0, which is not in the range of even numbers.

If x = 2, the hundreds digit would be 30 × 2 = 60, which is not an even digit.

If x = 4, the hundreds digit would be 30 × 4 = 120, which is an even digit.

So, the possible value for the tens digit is 4.

From this information, we have:

The thousands digit: Unknown

The hundreds digit: 1

The tens digit: 4

The units digit: 0

Therefore, the price of the scooter is $1,400.

To find the price of the scooter, let's break down the information provided step by step:

1. The scooter is priced between $1000 and $2000.
This means we are looking for a four-digit number between 1000 and 2000.

2. The price is a multiple of 10.
For the price to be a multiple of 10, the last digit must be 0.

3. All the digits in the price, except for the thousands digit, are even numbers.
This narrows down the possibilities for the tens and units digits to even numbers: 0, 2, 4, 6, or 8.

4. The value of the hundreds digit is 30 times the value of the tens digit.
Let's assume the tens digit is x, then the hundreds digit would be 30x.

Now, let's use this information to find the price of the scooter:

From step 2, we know the last digit is 0.
From step 3, the tens and units digits must be even.
From step 4, the hundreds digit is 30 times the tens digit.

To satisfy all these conditions, let's go through the possible values for the tens digit (x) that result in an even hundreds digit (30x) and an even unit digit (0):

For x = 2, the hundreds digit would be 30 x 2 = 60, resulting in a price of 2060.
For x = 4, the hundreds digit would be 30 x 4 = 120, resulting in a price of 2040.
For x = 6, the hundreds digit would be 30 x 6 = 180, resulting in a price of 2010.
For x = 8, the hundreds digit would be 30 x 8 = 240, resulting in a price of 2080.

Out of these options, only the price 2010 falls within the range of $1000 and $2000.

Therefore, the price of the scooter is $2010.