Solution:
Concept:
To solve this question, we will use the divisibility rule for 18
Divisibility of 18 – A number is divisible by 18 if the number is divisible by both 2 and 9.
From the question,
Divisibility of 9 – A number is divisible by 9 if the sum of all the digits is divisible by 9.
The total before tax given is
[tex]\text{ \$\#7.76}[/tex]
Step 1:
From the question, we can see that the total amount is divisible by 2 because the amount ends with an even number 6
Step 2:
Figure out the number so that it can be divisible by 9
Divisibility of 9 – A number is divisible by 9 if the sum of all the digits is divisible by 9.
The total before tax given is
Let the unknown number be
[tex]=x[/tex]
The sum of the number will be
[tex]\begin{gathered} d+7+7+6 \\ =d+20 \end{gathered}[/tex]
By try and error method
The only number divisible by 9 from 20 to 30 is
[tex]=27[/tex]
Hence,
[tex]\begin{gathered} d+20=27 \\ d=27-20 \\ d=7 \end{gathered}[/tex]
Therefore,
The unknown digit is = 7
Each cookie will cost
[tex]\begin{gathered} =\frac{\text{the total amount}}{\text{ number}} \\ =\frac{77.76}{18} \\ =\text{ \$4.32} \end{gathered}[/tex]
Hence,
Each cookie will cost = $4.32