How many gallons of fuel costing $1.15 a gallon must be mixed with a fuel costing $0.85 per gallon to get 40 gallons of a fuel that costs $1 per gallon? formulate an equation and then solve it in order to determine how many gallons of fuel costing $1.15. show all of your work.

Let x = the required number of gallons of fuel $1.15 per gallon.
From the problem description, you can write:
x($1.15)+20($0.85) = (20+x)($1.00) Simplify and solve for x.
1.15x+17 = 20+x Subtract x from both sides.

0.15x+17 = 20 Subtract 17 from both sides.
0.15x = 3 Finally, divide both sides by 0.15
x = 20
You would need to add 20 gallons of fuel $1.15 per gallon to 20 gallons of fuel $0.85 per gallon to obtain 40 gallons of fuel $1.00 per gallon.

This might not be correct but I hope it will be useful to you :3