Complex Math Problem, Can you solve!?

Question

Chris stopped for gas twice on a long car trip. The price of gas at the first station was $1.45 per gallon, and the price of gas at the second station was $1.55 per gallon. On the trip, Chris bought a total of 20 gallons of gas and spent $29.80. Let x = the number of gallons that Chris bought at the first station and y = the number of gallons Chris bought at the second station.

Solve the system of equations to find the number of gallons that Chris bought at the second station.

5 ?

8 ?

12 ?

20 ?

Answer 1

We know that Chris bought a total of 20 gallons, so x+y=20. We also know that the total cost of the gas was $29.80, so we have that 1.45x + 1.55y = 29.8. So all we need to do is solve. Solving the first equation for x:

x=20-y

Substituting into the second equation:

1.45(20-y) + 1.55y = 29.8
29-1.45y + 1.55y = 29.8
0.1y + 29 = 29.8
0.1y = .8
y = 8

Substituting this into the first equation:

x=20 - 8 = 12

So he bought 12 gallons at the first station and 8 gallons at the second station.

Answer 2

Find y:
y = $1.55(20 - x)
y = $31.00- $1.55x

Find x:
$1.45x + $31.00 - $1.55x = $29.80
$0.10x = $1.20
x = 12

Find y (plugging x with 12):
y = 20 - 12
y = 8

Answer: Chris bought 12 gallons at the first station and 8 gallons at the second station.

Proof (total spent for gas is $29.80):
= (12 gallons @ $1.45) + (8 gallons @ $1.55)
= $17.40 + $12.40
= $29.80

Answer 3

You can get two equations from the information:

1.45x + 1.55y = 29.80
x + y = 20

As you want to find y, substitute in the first equation (20-y) for x, multiply it out, rearrange, etc., then you'll find that y = 8.