Judy pays $29 for 8 gallons of gas and 2 bottles of water. Carmen pays $45 for 12 gallons of gas and 4 bottles of water. How much does one gallon of gas cost? How much does 1 bottle of water cost?

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31-01-2018
Mathematics

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Judy pays $29 for 8 gallons of gas and 2 bottles of water. Carmen pays $45 for 12 gallons of gas and 4 bottles of water. How much does one gallon of gas cost? How much does 1 bottle of water cost?

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perixwinkle perixwinkle · Answer 1 · 2018-01-31T06:49:35+01:00

g=gas
w=bottle of water

8g + 2w = 29
12g + 4w = 45
I'm going to use elimination to cancel out the variable w by multiplying the first equation by -2.

-16g - 4w = -58
12g + 4w = 45
-4g = -13
/-4 /-4
g = 3.25

Now plug it into an equation, any equation.
8 (3.25) + 2w = 29
26 +2w=29
w=1.5
Now to check, plug it into both equations if you want.

12 (3.25) + 4 (1.5)=45
39 + 6=45

One bottle of water is $1.50, while one gallon of gas is $3.25.