Word Problems! Any help appreciated!

[GlueStick1]

1. A 3x3x3 cube is formed by gluing together 27 standard dice. What is the smallest possible sum of all the numbers showing on the cube?

2. The sum of three numbers is 20. The first is 4 times the sum of the other two. The second is seven times the third. What is the prodct of all three?

3. Cindy was asked to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9, divided by 3, getting the answer 43. What is the correct answer supposed to be?

 

[galactus]

1. A 3x3x3 cube is formed by gluing together 27 standard dice. What is the smallest possible sum of all the numbers showing on the cube?

2. The sum of three numbers is 20. The first is 4 times the sum of the other two. The second is seven times the third. What is the prodct of all three?
Set up a system of equations and then substitute to get down to 1 variable.

Let x=the first number
Let y=the 2nd number
Let z=the 3rd number.

The sum of all 3 is x+y+z=20
x is 4 times the sum of y and z, so we have x=4(y+z).

The 2nd is 7 times the 3rd. so we have y=7z.

There's the system:

x+y+z=20
4(y+z)=x
7z=y

Solve the system.

3. Cindy was asked to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9, divided by 3, getting the answer 43. What is the correct answer supposed to be?

 

[Denis]

"A 3x3x3 cube is formed by gluing together 27 standard dice. What is the smallest possible sum of all the numbers showing on the cube?"

Get yourself 8 dice and make a 2x2x2 cube; then you'll see how it works;
apply same "strategy" to a 3x3x3.

"Cindy was asked to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9, divided by 3, getting the answer 43. What is the correct answer supposed to be?"

n = the certain number
(n - 3) / 9
what's the other one?