Question

in the table below, two operations are happening. whats the rule used to complete this table?
input\toutput
20\t13
30\t18
40\t23
50\t28
60\t33

Explanation:

Step1: Check input-output differences

$20-13=7$, $30-18=12$, $40-23=17$, $50-28=22$, $60-33=27$

Step2: Analyze the subtracted values

The differences (7,12,17,22,27) increase by 5 each time, which is $\frac{\text{Input}}{2} - 3$:
For input 20: $\frac{20}{2}-3=10-3=7$
For input 30: $\frac{30}{2}-3=15-3=12$

Step3: Derive the output rule

Output = Input - ($\frac{\text{Input}}{2}-3$) = $\frac{\text{Input}}{2}+3$
Verify: $\frac{20}{2}+3=10+3=13$, $\frac{30}{2}+3=15+3=18$, etc.

Answer:

Take half of the input value, then add 3 to get the output (mathematically: $\text{Output} = \frac{\text{Input}}{2} + 3$)