Answer:
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 ...
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.
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
