if 13 is added to a number and the sum is multiplied by 3, the result is 7 times the number decreased by 9.

Question

If 13 is added to a number and the sum is multiplied by 3, the result is 7 times the number decrease by 9. Find the number.

Answer 1

Hi Sabrina:

 

This is a single-variable algebra problem.  The tricky part is making sure you correctly translate the words into an equation.  As with all word problems, it's helpful to break it down into parts.

 

So:

1)  Let n stand in for "number"

2)  "If 13 is added to a number," so: n + 13

3)  "and the sum is multiplied by three," so: 3(n+13)

4)  "the result is," so:  3(n+13) =

5)   "7 times the number decreased by 9,"  so:  3(n+13) = 7n - 9

 

Now you can simply:=, moving numbers across the equal sign:

6)  3n + 39 = 7n - 9

7)  39 = 4n - 9

8)  48 = 4n

9)  12 = n

 

Seems right... but let's check it against our equation above:

3(12 + 13) = 7(12) - 9

3(25) = 84 - 9

75 = 75

 

We got it right!

Answer 2

3(x+13) = 7x - 9

3x + 39  = 7x - 9

  39 + 9   = 7x - 3x

   48     =  4x

   12     =   x

Check

3(12 + 13) = 7*12 - 9

36 + 39   =  84 - 9

75           =     75

Answer 3

(x+13)*3=7x-9 

3x+39=7x-9

-4x=-48

x=12