Answer: Each candy costs [tex]\$4.25[/tex] and each drink costs [tex]\$4[/tex]
Step-by-step explanation:
We are told Dominic bought 2 drinks and 5 candies, costing a total of [tex]\$29.25[/tex]:
[tex]2d+5c=\$29.25[/tex] (1)
Then, we are told Colton bought 8 drinks and 7 candies, costing a total of [tex]\$61.75[/tex]:
[tex]8d+7c=\$61.75[/tex] (2)
Now we have a system with two equations ans two unknowns. Let's solve it:
Multiplying (1) by -4:
[tex]-8d-20c=-\$117[/tex] (3)
Summing (2) and (3):
[tex]-13c=-\$55.25[/tex] (4)
Isolating [tex]c[/tex]:
[tex]c=\$4.25[/tex] (5) This is the cost of each candy
Substituting (5) in (1):
[tex]2d+5(\$4.25)=\$29.25[/tex] (6)
Isolating [tex]d[/tex]:
[tex]d=\$4[/tex] (7) This is the cost of each drink
The price of each drink is approximately $3.9 and the price of each candy is approximately $4.3 .
let
the price of a drink = x
the price of a candies = y
Therefore,
Dominic total expenses
Colton total expenses
Therefore,
2x + 5y = 29.25
8x + 7y = 61.75
multiply equation(i) by 4
8x + 20y = 117
8x + 7y = 61.75
20y - 7y = 117 - 61.25
13y = 55.75
y = 55.75 / 13
y = 4.28846153846
y ≈ $4.3
8x + 7y = 61.75
8x + 7(4.3) = 61.75
8x = 61.25 - 30.1
x = 31.15 / 8
x = 3.89375
x ≈ $3.9
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