Adealer has a lot that can hold 30 vehicles. in this lot, there are two available models, a and b. the dealer normally sells at least twice as many model a cars as model b cars. if the dealer makes a profit of $1300 on model a cars and $1700 on model b cars, how many of each car should the dealer have in the lot given that the total profit for the sale of both cars is $43,000?

a. 20 model a
10 model b

b. 10 model a
20 model b

c. 5 model a
25 model b

d. 16 model a
14 model b

i would appreciate if you explained!

The answer is a.   20 model A,    10 model B

a - the number of model A vehicles
b - the number of model B vehicles

A dealer has a lot that can hold 30 vehicles:
a + b = 30

The dealer makes a profit of $1300 on model A cars: 1300a
The dealer makes a profit of $1700 on model B cars: 1700b
The total profit for the sale of both cars is $43,000:
1300a + 1700b = 43000

The system of two equations:
a + b = 30
1300a + 1700b = 43000

Express the first equation in the term of a:
a = 30 - b
1300a + 1700b = 43000

Substitute a from the first equation into the second one:
1300(30 - b) + 1700b = 43000
39000 - 1300b + 1700b = 43000
39000 + 400b = 43000
400b = 43000 - 39000
400b = 4000
b = 4000/400
b = 10

Since a + b = 30 and b = 10, then
a + 10 = 30
a = 30 - 10
a = 20