SOLUTION: paul's calculator can make only two operations : add 12 to the number displayed ,or subtract 7 from it. today, it shows the number 1998. what is the minimal number of steps needed

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Question 205864: paul's calculator can make only two operations : add 12 to the number displayed ,or subtract 7 from it. today, it shows the number 1998. what is the minimal number of steps needed to display the number 2000 ?
A) 4 b) 12 c) 16 d) 21 e) 24
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
paul's calculator can make only two operations :
add 12 to the number displayed ,or subtract 7 from it.
today, it shows the number 1998.
what is the minimal number of steps needed to display the number 2000?
:
The resulting increase from repeating the two operations = +2
;
Let x = no. of +12 steps
Let y = no. of -7 steps
:
12x - 7y = 2
-7y = -12x + 2
7y = 12x - 2; multiplied by -1
y = 12%2F7x - 2%2F7
;
Substitute values for x until you get an integer value for y
x = 6 ea +12 steps
y = 12%2F7(6)- 2%2F7
y = 72%2F7 - 2%2F7
y = 70%2F7
y = 10 ea -7 steps
:
Total 16 steps