To find out how much Jason earned babysitting, we first need to calculate the total cost of the skateboard and helmet.
1. **Total Cost:**
- Skateboard: $45.50
- Helmet: $18.25
\[
\text{Total Cost} = \text{Skateboard} + \text{Helmet} = 45.50 + 18.25 = 63.75
\]
2. **Amount Earned from Mowing Lawns:**
Jason earned \( \frac{1}{3} \) of the total amount through mowing lawns.
\[
\text{Amount from Mowing Lawns} = \frac{1}{3} \times 63.75
\]
To calculate that:
\[
\frac{1}{3} \times 63.75 = 21.25
\]
3. **Amount Earned Babysitting:**
The rest of the money was earned through babysitting, which is \( \frac{2}{3} \) of the total amount.
\[
\text{Amount from Babysitting} = \text{Total Cost} - \text{Amount from Mowing Lawns}
\]
\[
\text{Amount from Babysitting} = 63.75 - 21.25 = 42.50
\]
Thus, Jason earned **$42.50** babysitting.