Question

find the largest of three consecutive integers such that 3 times the sum of the first and third integer is equal to 30 more than 4 times the second integer

Answer 1

So we have 3 integers, a,b, and c.
Using these integer variables, can you write equations that describe the problem?

Answer 2

3(a+c)=30+4(b)?

Answer 3

Yup!

Answer 4

Make use of the fact that the three integers are consecutive.

Answer 5

Since they're consecutive, try writing all of the variables in terms of the largest one (the one you're solving for).

Answer 6

umm.. would it be 3(a+ c=3)= 30+4(b+2)????

Answer 7

no i don't think that's it

Answer 8

Let's try redefining a and b:

If a, b, and c are consecutive, then that means:
a = c - 2
b = c - 1

That make sense?

Answer 9

yes that does

Answer 10

Try replacing a and b in your original equation with (c-1) and (c-2).

Answer 11

3(c-1+c)=30+4(c-1)

Answer 12

i ment 3(c-2+c)=30+4(c-1)

Answer 13

Good!
Now, just solve for c.

Answer 14

c=16

Answer 15

Yup! Good job.

Answer 16

thank you so much

Answer 17

thank you so much