How do I find the answer to this word problem

Question

Five times the sum of three consecutive integers is 150. What are the integers?

Answer 1

Let the 3 consecutive integers be X,X+1 & X+2

 

next we come up with an algebraic expression based  the condition given in the problem

 

5(3x+3) = 150

 

15x + 15 = 150

 

15x = 135

 

x= 9

 

now we know that the 3 integers are 9,10&11 by plugging in th value for X  we just found.

Answer 2

Hi Kylen, this is a confusingly worded problem, but easy to tackle:

 

 

 

• We know that 'five times the sum sum of three consecutive integers is 150,' but let's write that out in 'math' terms to better get an idea.
• We'll call our three consecutive integers 'a' 'b' and 'c'.

 

 

5 (a + b + c) = 150

 

 

From here, we can divide both sides by the number '5' to get rid of the coefficient in front of the parentheses:

 

 

(a + b + c) = 30

 

 

 

Now, we know that 'a' 'b' and 'c' are all consecutive integers, which means that all three follow each other, just like "1,2,3".

 

 

 

We need to find three numbers that follow each other and add up to 30. Let's use 10 as a starting point and go from there:

 

 

a = 10

b = 11

c = 12

 

a + b + c = 30

10 + 11 + 12 = 30

33 =/= 30

 

 

Looks like our answer was too high, so our choices should be a little lower. For our next attempt, let's try 9, 10 and 11:

 

 

a = 9

b = 10

c = 11

 

 

a + b + c = 30

9 + 10 + 11 = 30

30 = 30

 

 

Looks like that was our answer!

 

Answer 3

While Saul is correct that you can basically "guess" at the answer;

however, Mayuran's method is more useful since it can be applied

for pretty much any problem of this type.

 

Given 3 consecutive integers call them  x,  x+1,  and x+2

5 times the sum of 3 consecutive integers is 150 means:

 

5[x + (x+1) + (x+2)] = 150   divide both sides by 5

x+x+1+x+2 = 30                  combine like terms

3x + 3 = 30                          subtract 3 from both sides

3x = 27                                divide both sides by 3

x = 9

x+1 = 10

x+2 = 11

 

Your 3 integers are 9, 10, 11