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 1

Answer:each drink costs $0.55

Each slice of pizza costs $0.75

Step-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 - - - - - - - - - - - - 1

Your friend buys 3 drinks and 4 slices of pizza for $4.65. This means that

3x + 4y = 4.65 - - - - - - -- - - 2

Multiplying equation 1 by 3 and equation 2 by 4, it becomes

12x + 18y = 20.1

12x + 16y = 18.6

Subtracting, it becomes

2y = 1.5

y = 1.5/2 = 0.75

Substituting y = 0.75 into equation 1, it becomes

4x + 6 × 0.75 = 6.70

4x + 4.5 = 6.70

4x = 6.7 - 4.5 = 2.2

x = 2.2/4 = 0.55

Answer 2

Answer:

• drinks: $0.55
• pizza slices: $0.75

Step-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 = 6.70
• 3d +4p = 4.65

To 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 terms

Now, 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 6

The cost of a drink is $0.55; the cost of a slice of pizza is $0.75.