8th grade integers! help please!?

Question

four times the sum of three consecutive integers is 180. what are the integers?

the sum of an integer and the next greater integer is at most 13. write an ineqality to find the lesser integer. then solve for the lesser integer

* i really don't get it so i would really appreciate help! please & thank you

Answer 1

consecutive integers -
x = 1st number
x + 1 = 2nd number
x+ 2 = 3rd number

4 [ x + x + 1 + x + 2] = 180
4 [ 3x + 3] = 180
12x + 12 = 180
12x + 12 - 12 = 180 - 12
12x = 168
12x/12 = 168/12
x = 14

Go back to the top and the numbers are:
14, 15, 16

[I'm not too sure on this one, i'm probably wrong...]
x = smaller number
x + 1 = lager number

x + x + 1 = or < 13
2x + 1 =< 13
2x + 1 - 1 =< 13 - 1
2x =< 12
2x/2 =< 12/2
x =< 6

Answer 2

I believe the exercise here is to create a function to solve these problems.

four times the sum of three consecutive integers is 180

so if x is the first interger, then x+1 and x+2 are the next two consecutive integers. Therefor. 4 times the sum is given by:
4*(x+x+1+x+2)=180

now solve for x
4(3x+3)=180
12(x+1)=180
(x+1)=180/12=15
x+1-1=15-1
x=14, so the integers are 14, 15, and 16


the sum of an integer and the next greater integer is at most 13 (I'm not entirely sure what this is asking, but I'll try and solve for how I interpret it)

x+(x+1) <= 13
2x+1 <= 13
2x <= 12
x<=6

Answer 3

This sounds like a homework question. I'll help you work through the solution without taking it all the way.

The way to do this is to translate every phrase into math. So, "four times the sum of (...)" means "4 * (...)" and "the sum of three consecutive integers" can be expressed as "x + (x+1) + (x+2)". So you can turn the first sentence into "4 * (x + (x+1) + (x+2)) = 180" and solve for x, and the answer comes from there.

The next question can be answered in basically the same way, but it revolves around finding a way to express "at most 13" mathematically. The rest is simple.

Answer 4

1) integer == x
next integer == x + 1
etc.

4 * (x + x + 1 + x + 2) = 180
(3x + 3) = 180/4 = 45
3x = 45 - 3 = 42
x = 42/3 = 14

Integers are 14, 15, 16.

2) x + x + 1 <= 13
2x + 1 <= 13
2x <= 13-1
2x <= 12

You can get it from there. The key to word problems is to look for the "is" -- that's where the equals sign (or inequality sign) goes.

Answer 5

easy, we set it up this way:

4(x + (x + 1) + (x + 2)) = 180

where x, x+1, and x+3 are the consecutive integers.

we combine like terms inside the perentesees which gives us:

4(3X + 3) = 180

then we distribute the 4 to get:

12X + 12 = 180

subtract 12 from both sides and divide by 12, this gives us X = 14

so the three consecutive integers are 14, 15, and 16

Answer 6

8th Grade Integers

Answer 7

1) let the consec integers be x, x+1, x+2
Therefore, 4(x+x+1+x+2) = 180
3x+3=45 (Dividing both sides by 4)
3x=42
x=14
Cant help u with the 2nd one.
Hope it helps

Answer 8

i won't solve it out but this is how the first one looks like:
4(x + (x + 1) + (x + 2)) = 180

x is your first digit

x + (x + 1) > 13


hope this helps

Answer 9

i guarantee you will NEVER need this in real life. i mean, our president, can't even spell MATH. rich people do stupid stunts for lots of money, while college graduates flip burgers. good luck...

oh, and i don't know. i was good in algebra, but that was 16 years ago.

Answer 10

uh I'm in 8th grade and I don't even know what you're talking about.