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den301095 [7]
3 years ago
15

Michelle decides to mix grades of gasoline in her truck. She puts in 9 gallons of regular and 11 gallons of premium for a total

cost of $62.38. If premium gasoline costs $0.18 more per gallon than regular, what was the price of each grade of gasoline?
Mathematics
1 answer:
7nadin3 [17]3 years ago
7 0

Hi there! :)

Answer:

Regular = $3.02, Premium = $3.20

------------------------------------------------

Let x = regular gasoline

x + 0.18 = premium gasoline

Write an algebraic equation to express the scenario:

9(x) + 11(x + 0.18) = 62.38

Distribute:

9x + 11x + 11(0.18) = 62.38

Combine like terms and simplify:

20x + 1.98 = 62.38

Subtract 1.98 from both sides:

20x = 60.4

Divide both sides by 20:

x = $3.02

Substitute this value in the equation for premium gasoline:

(3.02) = .18 = $3.20

The prices of each type of gasoline are:

Regular = $3.02, Premium = $3.20

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              u = t² + 6t - 20
         + 20            + 20
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------------------------------------------------------------------------------------------------------------------
Part A: g(t) = 48.8t + 28           h(t) = -16t² + 90t + 50
            | t |   g(t)  |                          |  t  |  h(t)  |
            |-4|-167.2|                          | -4 | -566 |
            |-3|-118.4|                          | -3 | -364 |
            |-2| -69.6 |                          | -2 | -194 |
            |-1| -20.8 |                          | -1 |  -56  |
            |0 |   -28  |                          |  0  |   50  |
            |1 |  76.8 |                          |  1  |  124 |
            |2 | 125.6|                          |  2  | 166  |
            |3 | 174.4|                          |  3  | 176  |
            |4 | 223.2|                          |  4  | 154  |
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Part B: The solution from Part A means that you have to find two solutions in order to know where the solutions of the two functions are located at.
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