4d + 4b = 14 and 8d + 3b = 20.50 are the system of equations that can be used to find the price of one drink and the price of one bag of popcorn
Price of one drink is $ 2 and price of one bag of popcorn is $ 1.5
<h3><u>Solution:</u></h3>
Let "d" be the price of one drink
Let "b" be the price of one bag of popcorn
Given that Justin spends a total of $14.00 on 4 drinks and 4 bags of popcorn.
<em><u>So we can frame a equation as:</u></em>
4 drinks x price of one drink + 4 bags of popcorn x price of one bag of popcorn = $ 14.00
4d + 4b = 14 ------ eqn 1
Given that Lincoln spends a total of $20.50 on 8 drinks and 3 bags of popcorn
<em><u>So we can frame a equation as:</u></em>
8 drinks x price of one drink + 3 bags of popcorn x price of one bag of popcorn = $ 20.50
8d + 3b = 20.50 ---- eqn 2
Thus eqn 1 and eqn 2 are the system of equations that can be used to find the price of one drink and the price of one bag of popcorn
Let us solve eqn 1 and eqn 2 to find values of "d" and "b"
Multiply eqn 1 by 2
8d + 8b = 28 --- eqn 3
Substract eqn 2 from eqn 3
8d + 8b = 28
8d + 3b = 20.50
(-) ------------------------
5b = 7.5
<h3>b = 1.5</h3>
Substitute b = 1.5 in eqn 1
4d + 4(1.5) = 14
4d = 8
<h3>d = 2</h3>
Thus price of one drink is $ 2 and price of one bag of popcorn is $ 1.5