I'm having a hard time coming up with the right equation to solve this one.

E-Z Stop Fast Gas sold $10,957 worth of gasoline yesterday. Regular grade sold for $2.30 a gallon and premium grade sold for $2.55 a gallon. If the station sold 420 more gallons of regular than of premium, how many gallons of regular were sold?

x=Regular Grade

y=Premium Grade

x(2.30)+y(2.55)=10,957
x=y+420

y+420(2.30)+y(2.55)=10,957
2.30y+966+2.55y=10,957
4.85y+966=10,957
4.85y=9991
y=2,060 Gallons of Premium Grade

x=2,060+420
x=2,480 Gallons of Regular Grade

Hope this helps :)

5/6

i need help with square feet and cubic

To solve this problem, you need to set up and solve a system of equations. Let's assign variables to the unknown quantities to make it easier to represent the problem mathematically.

Let's say R represents the number of gallons of regular grade gasoline sold, and P represents the number of gallons of premium grade gasoline sold.

According to the problem, the total value of gasoline sold is $10,957. We can express this as an equation:

2.30R + 2.55P = 10,957

Next, we are given that the station sold 420 more gallons of regular than premium. This can be expressed as another equation:

R = P + 420

Now we have a system of equations. To solve it, we can substitute the value of R in the first equation with the value of P + 420 from the second equation:

2.30(P + 420) + 2.55P = 10,957

Simplifying the equation:

2.30P + 966 + 2.55P = 10,957
4.85P + 966 = 10,957

Subtracting 966 from both sides:

4.85P = 9,991

Dividing by 4.85:

P = 2,057.53

Since the number of gallons must be a whole number, we round down to 2,057.

Therefore, the number of gallons of premium gasoline sold is 2,057.

To find the number of gallons of regular gasoline sold, substitute this value back into the equation R = P + 420:

R = 2,057 + 420
R = 2,477

So, 2,477 gallons of regular gasoline were sold.