The concession stand at football games sells pizza and drinks. You buy 4 drink and 6 slices of pizza for $6.70. Your friend buys 3 drinks and 4 slices of pizza for $4.65. How much is each drink and slice of pizza?

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Question:

The concession stand at football games sells pizza and drinks. You buy 4 drink and 6 slices of pizza for $6.70. Your friend buys 3 drinks and 4 slices of pizza for $4.65. How much is each drink and slice of pizza?

Answer:drinks: $0.55pizza slices: $0.75Step-by-step explanation:Let d represent the cost of a drink, and p represent the cost of a pizza slice. Then the two purchases can be represented by ...4d +6p = 6.703d +4p = 4.65To solve these equations by elimination, choose a variable to eliminate and look at the coefficients of that in the two equations. If we choose to eliminate p, we see the coefficients of p are 6 and 4. The least common multiple of these numbers is 12. We can multiply the first equation by -2 and the second equation by +3 and the resulting coefficients of p will be -12 and +12. Adding the results of these multiplications will make the p terms add to zero. -2(4d +6p) +3(3d +4p) = -2(6.70) +3(4.65) -8d -12p +9d +12p = -13.40 +13.95 . . . . . . . . . eliminate parentheses d = 0.55 . . . . . . . . . collect termsNow, we can substitute this value into either equation to find the value of p. Using the first equation, we get ... 4(0.55) +6p = 6.70 6p = 4.50 . . . . . . . . . subtract 2.20 p = 0.75 . . . . . . . . . . divide by 6The cost of a drink is $0.55; the cost of a slice of pizza is $0.75.

answer from sqdancefan

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Answer:each drink costs $0.55Each slice of pizza costs $0.75Step-by-step explanation:Let x represent the cost of each drink.Let y represent the cost of each slice of pizza.You buy 4 drink and 6 slices of pizza for $6.70. This means that 4x + 6y = 6.70 - - - - - - - - - - - - 1Your friend buys 3 drinks and 4 slices of pizza for $4.65. This means that 3x + 4y = 4.65 - - - - - - -- - - 2Multiplying equation 1 by 3 and equation 2 by 4, it becomes12x + 18y = 20.112x + 16y = 18.6Subtracting, it becomes2y = 1.5y = 1.5/2 = 0.75Substituting y = 0.75 into equation 1, it becomes4x + 6 × 0.75 = 6.704x + 4.5 = 6.704x = 6.7 - 4.5 = 2.2x = 2.2/4 = 0.55

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