Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast to $3 in the mid-US, to $5 on the west coast.

(a) If they used twice as much gas in the mid-US than on either coast combined, and they spend $515 on gas to purchased 150 gallons of gas, how many gallons of gas did they buy at each price?

The answer to this question is East Coast - 35 gal, Mid-US - 100 gal, West Coast - 15 gal.

(b) On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price? I don't know the answer to this one

The quantity of fuel bought at $4 is 40.84 gallons

The quantity of fuel bought at $3 is 116.699 gallons

The quantity of fuel bought at $5 is 17.505 gallons

Step-by-step explanation:

Here we have

Gas used on East coast = X gallons

Gas consumed in the mid-US = Y gallons

Gas consumed in the West coast = Z gallons

Where Y = 2 * (X + Z) ... (1)

4·X + 3·Y + 5·Z = 515 ... (2)

X + Y + Z = 150 ... (3)

Therefore substituting for Y in equation (3) we have

X + 2 * (X + Z) + Z = 150

3·X + 3·Z = 150

X = (150 - 3·Z) / 3 = 50 - Z

Therefore, equation (2) becomes;

4· (50 - Z) + 3· (2 * ((50 - Z) + Z)) + 5·Z = 515

200 - 4·Z + 300 - 6·Z + 6·Z + 5·Z = 515

500 + 2·Z = 515

Z = 15

X = 50 - Z = 50 - 15 = 35

Y = 2 * (X + Z) = 2 * (35 + 15) = 2 * 50 = 100

(b) Whereby the bought 174 gallons based on the same ratio as in part (a), we have;

Ratio in part (a) is given as follows;

Proportion of Z gallons = 15/150 = 1/10

Proportion of X gallons = 35/150 = 7/30

Proportion of Y gallons = 100/150 = 2/3

Therefore the proportion of 174 gallons that was consumed in the East coast, X gallons = (7/30) * 174 = 203/5 gallons = 40.6 gallons

The proportion of 174 gallons that was consumed in the mid-US, Y gallons = (2/3) * 174 = 116 gallons

The proportion of 174 gallons that was consumed in the West coast, Z gallons = (1/10) * 174 = 87/5 gallons = 17.4 gallons

Based on price of per gallon, we have

The proportion of $515 that was consumed in the East coast on X gallons = $4 * 35 = $140

Proportion = 140/515 = 28/103

The proportion of $515 that was consumed in the mid-US on Y gallons = $3 * 100 = $300

Proportion = 300/515 = 60/103

The proportion of $515 that was consumed in the West coast on Z gallons = $5 * 15 = $75

Proportion = 75/515 = 15/103

Therefore, the quantity of fuel bought at $4 = ((28/103) * 601) / 4 = 40.84 gallons

The quantity of fuel bought at $3 = ((60/103) * 601) / 3 = 116.699 gallons

The quantity of fuel bought at $5 = ((15/103) * 601) / 5 = 17.505 gallons.