Amelia and Nora go to the movie theater and purchase refreshments for their friends.
Amelia spends a total of $18.00 on 6 bags of popcorn and 3 drinks. Nora spends a total of $31.25 on 5 bags of popcorn and 9 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.
Answers
GiveN:
Amelia spends a total of $18.00 on 6 bags of popcorn and 3 drinks.
Nora spends a total of $31.25 on 5 bags of popcorn and 9 drinks.
What to do?
We have to write the above system of simultaneous linear equation in two variables.
And solving for the price of popcorn and drink individually.
Step-wise-Step Explanation:
Let the price of popcorn be x and the price of drink be y. Then according to above conditions:
6x + 3y = $18.00
5x + 9y = $31.25
Multiplying 3 with equation (1),
⇒ 3(6x + 3y) = $54
⇒ 18x + 9y = $54
Subtracting eq. (2) from eq. (1),
⇒ 18x + 9y - (5x + 9y) = $54 - 31.25
⇒ 18x + 9y - 5x - 9y = $22.75
⇒ 13x = $22.75
⇒ x = $1.75
Plugging the value of x in eq. (1),
⇒ 6(1.75) + 3y = $18
⇒ 10.5 + 3y = $18
⇒ 3y = $7.5
⇒ y = $2.5
Hence,
- Price of 1 popcorn box = $1.75
- Price of 1 drink = $2.50
Answer:
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