Luke, Paul, Vincent and Tommy went shopping with a total of $609. After shopping, they had a total of $185 left. Paul spent $50. The amount Vincent spent was ⁴₇ the amount spent by Luke. The total amount spent by Luke and Paul was $-12 less than the total amount spent by Vincent and Tommy. How much did Luke and Tommy spend altogether?

	Luke	Paul	Vincent	Tommy	Total
Before					$609
Change	- 7 u	- $50	- 4 u	- ?	- $424
After					$185

Total amount that Luke, Paul, Vincent and Tommy spent
= 609 - 185
= $424

Total amount that Luke and Paul spent
= 7 u + 50

Total amount that Vincent and Tommy spent
= 7 u + 50 + -12
= 7 u + 38 

Total amount that Luke, Paul, Vincent and Tommy spent
= 7 u + 50 + 7 u + 38
= 14 u + 88 

14 u + 88 = 424
14 u = 424 - 88
14 u = 336 

1 u = 336 ÷ 14 = 24

Total amount that Paul and Vincent spent
= 4 u + 50
= 4 x 24 + 50
= 96 + 50
= $146

Total amount that Luke and Tommy spent
= 424 - 146
= $278

Answer(s): $278