一个三明治的价格是一个派的 5 倍。伊克（Iker）拥有的钱刚好够买 4 个这样的三明治和 8 个这样的派。然而，他只想买派。他用自己钱的 $\frac{3}{5}$ 最多可以买多少个派？

1. Express the cost of a sandwich in terms of pies

Let the cost of $1$ pie be $1$ unit.
Cost of $1$ sandwich = $5$ units.

2. Calculate the total amount of money Iker has in terms of pie units

Total money = Cost of $4$ sandwiches + Cost of $8$ pies
Total money = $4 \times 5$ units + $8 \times 1$ unit
Total money = $20$ units + $8$ units = $28$ units.

3. Calculate the amount of money Iker wants to spend

Amount to spend = $\frac{3}{5}$ of Total money
Amount to spend = $\frac{3}{5} \times 28$ units = $\frac{84}{5}$ units = $16.8$ units.

4. Determine the greatest number of pies he can buy

Since $1$ pie costs $1$ unit, he can buy $16.8$ pies with this amount.
The greatest whole number of pies he can buy is $16$.