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?

Question

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

Answer 1

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

Answer 2

for your second question set up a ratio equation:

x/120 = 1/2.5

solve for x

Answer 3

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