Question

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

Answers

Reiny
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
Reiny
for your second question set up a ratio equation:

x/120 = 1/2.5

solve for x
Damon
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

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