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. 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?

A) The amount of gas they bought on each coast;

East Coast = 35 gallons

Mid-US = 100 gallons

West Coast = 15 gallons

B) The amount of gas they bought on each coast on the return journey;

East Coast = 37 gallons

Mid-US = 116 gallons

West Coast = 21 gallons

Step-by-step explanation:

Complete Question

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

Solution

Let the amount of fuel bought on the east coast = x gallons

Let the amount of fuel bought on the mid-coast = y gallons

Let the amount of fuel bought on the west coast = z gallons

a) - They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $515 on gas to purchase 150 gallons of gas.

Total gallons purchased = x + y + z = 150

Total amount spent = 4x + 3y + 5z = 515

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 150

3x + 3z = 150

Divide through by 3

x + z = 50 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 515

4x + 6x + 6z + 5z = 515

10x + 11z = 515 (eqn **)

x + z = 50

10x + 11z = 515

Solving the simultaneous equation,

x = 35 gallons

z = 15 gallons

y = 2x + 2z = 2(35 + 15) = 100 gallons

B) On the return journey, the ratio between x, y and z is still the same, but the total gallons and total amount spent is now different.

They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $601 on gas to purchase 174 gallons of gas.

Total gallons purchased = x + y + z = 174

Total amount spent = 4x + 3y + 5z = 601

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 174

3x + 3z = 174

Divide through by 3

x + z = 58 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 601

4x + 6x + 6z + 5z = 601

10x + 11z = 601 (eqn **)

x + z = 58

10x + 11z = 601

Solving the simultaneous equation,

x = 37 gallons

z = 21 gallons

y = 2x + 2z = 2(37 + 21) = 116 gallons

Hope this Helps!!!

nope.   happens to me as well.

-aparri