I am thinking of a number.It is a multiple of 3 but not 6.It is greater than 25^2 but less than 30^2.The units digit is a perfect square and the sum of the other two digits is the square root of 81. What is my number?

A three-dimensional model of a city has a scale of 1 inches=2.5 foot.the actual distance between the two buildings is 120 feet. what is the distance on the scale model?

Any help or advice please?
anything would help

It is greater than 25^2 but less than 30^2 --> hundreds digit must be 6,7, or 8

The units digit is a perfect square --> unit digit must be 1,4,or 9

the sum of the other two digits is the square root of 81 --> the sum of the first 2 numbers must be 9

so there are only 9 possibilities

631 634 639
721 724 729
811 814 819

of those 639 729 819 divide by 3 but not by 6

so you have 3 such numbers

639 729 and 819

for your second question set up a ratio equation:

x/120 = 1/2.5

solve for x

factor is 3, not 2 (because 2 and 3 is 6)

between 625 and 900
x y z
x+y = 9
z is 4, or 9 so 9 because 2 not a factor
so
x y 9
x is 6,7 or 8 (between 625 and 900)
so y is 3, 2 or 1
so
639
729
819 are 3 candidates
which can you divide by 3?
639 yes
729 yes
819 yes
I can not narrow that down to one.

120 ft * (1 inch/2.5 ft) = 48 inches

To find the number, let's go through each condition and narrow down the possibilities step by step:

1. It is a multiple of 3 but not 6: This means the number has to be a multiple of 3 but not a multiple of 6. The multiples of 3 greater than 25^2 but less than 30^2 are 27, 30, 33, and so on.

2. It is greater than 25^2 but less than 30^2: The square of 25 is 625, and the square of 30 is 900. So the number we are looking for falls between these two values.

3. The units digit is a perfect square: The perfect squares only have digits 0, 1, 4, or 9 as their units digit.

4. The sum of the other two digits is the square root of 81: The square root of 81 is 9. This means the other two digits of the number must sum up to 9.

Combining these conditions, we can start narrowing down the possibilities:

- The number has to be greater than 625 and less than 900.
- The units digit can only be 1 or 9.
- The sum of the other two digits has to be 9.

By considering these conditions, the possible numbers that meet all the criteria are 639 and 963.

Therefore, your number could be either 639 or 963.

As for the second question about the scale model:

Given that 1 inch is equal to 2.5 feet, we can use a proportion to find the distance on the scale model:

Scale ratio: 1 inch = 2.5 feet
Actual distance: 120 feet

Let's set up the proportion:

1 inch / 2.5 feet = x inches / 120 feet

Cross-multiplying, we get:

2.5 feet * x inches = 1 inch * 120 feet

Simplifying further:

2.5x = 120

Dividing both sides by 2.5:

x = 120 / 2.5

x = 48

Therefore, the distance on the scale model would be 48 inches.

I hope this helps! Let me know if you have any further questions or need further assistance.