Zach had 80 more guppies than Ken at first. Ken gave 24 of his guppies to Zach. Zach had 3 times as many guppies as Ken after that. How many guppies did Zach have at first? Ans: ___

1. Find the new difference in the number of guppies between Zach and Ken after the transfer.

Since Ken gave $24$ guppies to Zach, the difference between them increases by $24 \times 2 = 48$.
New difference $= 80 + 48 = 128$

2. Use the final ratio to find the value of 1 unit.

In the end, Zach has $3$ units and Ken has $1$ unit.
Difference in units $= 3 - 1 = 2$ units
$2 \text{ units} = 128$
$1 \text{ unit} = 128 \div 2 = 64$

3. Calculate the number of guppies Zach had at first.

Zach's guppies in the end $= 3 \text{ units} = 3 \times 64 = 192$
Zach's guppies at first $= 192 - 24 = 168$