Given,
The number of miles covered by the car in one gallon is 15 miles.
The cost of one gallon of gas is $3.17.
The distance of vacation place place is 290 miles away.
The total distance has to cover in round trip is,
![\text{Total distance covered = 290+290=580 miles}](https://img.qammunity.org/2023/formulas/mathematics/college/9lwc7tgfdevnrndc140pg822e8zfvyfm2a.png)
The quantity of gas required to cover 580 miles of distance.
![\text{quantity of required gas=}(580)/(15)=38.67\text{ gallons}](https://img.qammunity.org/2023/formulas/mathematics/college/4n11cym2o893o79ev86mk9sukb366cvg52.png)
The cost required for gas is ,
![\text{Cost of gas =38.67}*3.17=122.573333](https://img.qammunity.org/2023/formulas/mathematics/college/rlgovkh5gfv1bsq67cgkpqmvbi9nkcz1pe.png)
Hence, $122.57 (approximately) money will Thomas have to budget for the gas used on this round trip.