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
![\text{ \$\#7.76}](https://img.qammunity.org/2023/formulas/mathematics/college/niqtdtbs52zb3tsi6g898kj94eda6g74db.png)
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
![=x](https://img.qammunity.org/2023/formulas/mathematics/college/1ye1eo60321kt0irebsbvlxoc6mkb0xjkb.png)
The sum of the number will be
![\begin{gathered} d+7+7+6 \\ =d+20 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/i7ozqcn77nk29cbn77d28iye37vhp6l7tw.png)
By try and error method
The only number divisible by 9 from 20 to 30 is
![=27](https://img.qammunity.org/2023/formulas/mathematics/college/qg4yj61pjszdmraeaoi2scyv1466617e2i.png)
Hence,
![\begin{gathered} d+20=27 \\ d=27-20 \\ d=7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/j01gbd7etjjykrn54sjdx5skivq4lxnzct.png)
Therefore,
The unknown digit is = 7
Each cookie will cost
![\begin{gathered} =\frac{\text{the total amount}}{\text{ number}} \\ =(77.76)/(18) \\ =\text{ \$4.32} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/1dgvg4lcla7cnsp4n5bn1bub4ntweba84h.png)
Hence,
Each cookie will cost = $4.32