Answer:
The cost of a beverage = $4
The cost of a popcorn bag = $5.5
Step-by-step explanation:
Let p denote popcorn and d denote drink.
Harper purchased 10 popcorn bags and 6 drinks, totaling $79 ➡ 10p + 6d = $79.
Damian paid $36.50 for 3 bags of popcorn and 5 drinks ➡ 3p + 5d = $36.50.
Next, multiply the first equation by -3 and the second by 10:
-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237
10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365.
Now combine the modified equations:
30p + 50d -30p - 18d = $365 - $237 (-30p cancels out)
32d = $128, then divide each side by 32:
32 ÷ 32d = 32 ÷ $128 ➡ d = 4.
If d = 4 indicates a drink costs $4, we can find the popcorn bag's price as follows:
3p + 5d = $36.50 (substituting d with 4)
3p + 4×5 = $36.50
3p + 20 = $36.50
3p = $36.50 - 20
3p = 16.50, then divide both sides by 3:
p = $5.5.
