What is the original number?

Question

A certain number is increased by 15 and the result is doubled. The new result is 6 more than 3 times the original number.

 

A. 4

B. 9

C. 10

D. 12

E. 24

Answer 1

let x = the number

 

then do what the problem says

 

increase by 15

 

x + 15

 

then double

 

2(x+15)

 

2x + 30  this result is six more than 3 times the original number

 

3x + 6 (this is six more than 3 times the original number)

 

now set them equal and solve for x

 

2x +30 = 3x + 6

 

x = 24

 

see if it works

 

increase by 15

 

39

 

double

 

78

 

3 times the original number plus 6

 

3 times 24

 

72

 

plus 6

 

78

 

so we get 78 either way

 

therefore, 24 is the correct value for x

 

 

Answer 2

Cassie, let's set up the equation first. We took a number and added 15. If we say n = the original number, then that's n + 15. Double the result looks like 2(n + 15). Six more than 3 times the number is 3n + 6, right?

 

So, we have that 2(n + 15) = 3n + 6. 

 

Can you solve it from here?