Algebra 2 finding numbers question

Question

Two dump trucks have capacities in the ratio 2 to 3. The larger dump truck hold 4 tons more than the smaller truck. What is the capacity of each dump truck?

I am having trouble knowing how to do this question, so an explanation with steps would be greatly appreciated!

Thank you!!

Answer 1

Let the amount of both trucks be X in pounds

Larger is (3/5)X and the smaller is (2/5)X

(3/5)X = (2/5)X + 8000 <-- 4 tons more

3X = 2X + 40000

X=40000

Larger truck has 3/5*40000=24000 lbs = 12 tons

Smaller truck has 2/5*40000=16000 lbs= 8 tons

Answer 2

capacity of smaller truck = x

capacity of larger truck = x + 4

ratio of capacities is 2 to 3

so form the following proportion:

2 x

-- = ----

3 x+ 4

cross-multiply and solve:

2(x+4) = 3x

2x + 8 = 3x

8 = x

x+4 = 12

capacity of two dump trucks is 8 and 12 tons.