Question

Dominic went into a movie theater and bought 2 drinks and 5 candies, costing a total of $29.25. Colton went into the same movie theater and bought 8 drinks and 7 candies, costing a total of $61.75. Determine the price of each drink and the price of each candy.

Answer 1

Answer: Each candy costs $\ 4.25$ and each drink costs $\ 4$

Step-by-step explanation:

We are told Dominic bought 2 drinks and 5 candies, costing a total of $\ 29.25$:

$2d+5c=\ 29.25$ (1)

Then, we are told Colton bought 8 drinks and 7 candies, costing a total of $\ 61.75$:

$8d+7c=\ 61.75$ (2)

Now we have a system with two equations ans two unknowns. Let's solve it:

Multiplying (1) by -4:

$-8d-20c=-\ 117$ (3)

Summing (2) and (3):

$-13c=-\ 55.25$ (4)

Isolating $c$:

$c=\ 4.25$ (5) This is the cost of each candy

Substituting (5) in (1):

$2d+5(\ 4.25)=\ 29.25$ (6)

Isolating $d$:

$d=\ 4$ (7) This is the cost of each drink