some 7th grade math questions>Ex:How many laps must a person run around a quarter-mile track to run 91/2 mi.

Question

1.. a number is balanced if exactly one digit is the sum of all the other digits. What is the greatest three-digit balanced number?

2.. The Sound Of Music, one of the all-time favorite movies, won an Academy Award in what year? The sum of the digits of the year is 21, the tens' digit is greater than the ones' digit, and the product of the digits is 270.

3.. The number of Supreme Court Justices is the greatest common factor of 19 and 27. How many Supreme Court Justices are there?

4.. How many laps must a person run around a quarter-mile track to run 9 1/2 miles?

5.. If a regular octahedron has a surface area of 32 square inches, what is the surface area of each face?

for number 3 instead of 19 its suppose to be 18

Answer 1

a) 9 1/2 divided by 1/4 = 38 laps

b) A three digit number is composed of "x" in the hundreds column, "y" in the tens, and "z" in the ones...i.e. x,y,z. To maximize this number, we need "x" to be a "9". Then, 9 needs to equal the sum of the other two. So, 5/4, 6/3, 8/1 etc. So, an 8 needs to be in the tens, and 1 in the ones.

981 is the largest balanced number.

c) a * b * c * d = 270. We know that c is greater than d. We know that a + b + c + d = 21.

None of the digits can be 0 since that would make the product 0
We know the first two digits are "1" and "9"

Therefore:

1 * 9 * c * d = 270
c * d = 30

What two numbers will make thirty? 6 / 5
Tens is larger, so 1965.

Check: 1 + 9 + 6 + 5 = 21
1 x 9 x 6 x 5 = 270

d) Greatest common factor of 19 and 27. Factors of 19 are 19 and 1. Factors of 27 are 1,3,9, and 27.

(There are 9 supreme court justices, so did you mean GCF of *18* and 27???)

e) I answered this first since it was your subject line...answer a.


f) Area = 32 sq inches / 8 surfaces = 4 square inches per face.

Answer 2

I'll try to help without giving you the answers.

1. What's the greatest 3 digit number? That's 999. Is that balanced? No, because the biggest number, 9, doesn't equal the other two combined, 9 + 9.

you can come up with two other numbers that equal nine. Then make that number as high as possible. 927 would work, but so would 945...

2. well it wasn't done in the 1700s, was it? It was done in the 1900s, and I think it was the 1960s or 1970s.

Give me two numbers, 196? and 197?, that add up to 21. Then get multiplying and see what equals 270. Hint: that zero probably came from a 5 or a 0.

3. Dude, question is wrong, there is no GCF between 19 and 27. Should be 18. What number goes into 18 and 27?

And why aren't you good at your times tables?!?

4. Ok, a quarter mile means four laps to a mile. How many is 9 miles? Then add two more laps for the half mile at the end.

5. An octohedron has 8 sides, that's what octo means. Like octopus. If it has 8 sides, and they all add up to 32, what's each side?

AND WHY DON'T YOU KNOW YOUR TIMES TABLES? Until you learn them, math will totally suck for you. Get memorizing! Do it now! Put down the videogames! RUN FOR YOUR LIFE!

Answer 3

(1) 981 (2)1965 (3) if you made a mistake in this question.According to the question ,the answer is only 1 (4) 37 (5) 4 sq.inches

Answer 4

Check #3: is it 19 or 99?