Question

The sum of three consecutive whole numbers is a number between 70 and 100. Give three possible starting numbers for the group of three consecutive whole numbers. Solve and show all working out.

Answer 1

First, express the three consecutive whole numbers algebraically. Hint: were we to begin with 20, the next consecutive whole number would be 20+1 = 21.

Answer 2

So like, x + x +1 + x +2 or something?

Answer 3

Yes, that's right! Simplify that result algebraically. This is your "sum."

This sum is between 70 and 100. How would you express that algebraically?

Answer 4

x + x + 1 +x +2 = 30?

Answer 5

Why 30? We are told that the sum is between 70 and 100. Could you write an inequality expressing this fact?

Answer 6

x+x+1+x+2 =70 -100?

Answer 7

But that's not an inequality, is it? What does "an inequality" mean to you?

Answer 8

I'm not too sure what it means....

Answer 9

"The sum lies between 70 and 100" translates into the inquality

\[70\le Sum \le100\]

Answer 10

So, whatever your Sum is, it has to be 70 or greater or 100 or less.

Answer 11

so x+x+1+x+2 = more than 70 and less than 100?

Answer 12

Yes, that's right.

What is the sum of x, x+1 and x+2?

Answer 13

Except that you mean "equal to or more than 70 or equal to or less than 100."

Answer 14

3x + 3 = equal to or more than 70 or equal to or less than 100?

Answer 15

Yes, and expressing that algebraically, we get \[70\le3x+3\le100\]

Answer 16

By "algebraically," I meant "symbolically."

Answer 17

Remember, x will be the starting value of 3 consecutive numbers whose sum is 70 or greater , up to 100.

Answer 18

What's our next step in solving for x?

Answer 19

minus the three from the LHS and use the inverse operation on the RHS?

Answer 20

Try this, please: just subtract 3 from the left term, the middle term and the right term (3 separate subtractions).

Answer 21

@kapow...I'd be happy to help you finish this problem, but would appreciate faster responses on your part.

Answer 22

Sorry about that! I will try to be more prompt with my replies!

Answer 23

Sorry too. But I've waited and waited for you to subtract 3 from those 3 terms of the inequality without seeing any action on your part. Perhaps we could continue later.

Answer 24

Sure! Thank you for trying to help! :)

Answer 25

Next time you're not going to responding right away, please let me know. i believe I spent about ten minutes waiting for a response from you. That's time i could have spent helping other students.