The price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25
Solution:
Let d" be the price of 1 drink
Let "p" be the price of 1 pretzel
Given that, Isabella went into a movie theater and bought 3 drinks and 10 pretzels, costing a total of $54.50
Therefore, we can frame a equation as,
3 x price of 1 drink + 10 x price of 1 pretzel = 54.50
[tex]3 \times d + 10 \times p = 54.50[/tex]
3d + 10p = 54.5 ---------- eqn 1
Jason went into the same movie theater and bought 9 drinks and 5 pretzels, costing a total of $57.25
9 x price of 1 drink + 5 x price of 1 pretzel = 57.25
[tex]9 \times d + 5 \times p = 57.25[/tex]
9d + 5p = 57.25 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 3
9d + 30p = 163.5 ----- eqn 3
Subtract eqn 2 from eqn 3
9d + 30p = 163.5
9d + 5p = 57.25
( - ) -----------------------
25p = 106.25
p = 4.25
Substitute p = 4.25 in eqn 1
3d + 10(4.25) = 54.5
3d + 42.5 = 54.5
3d = 54.5 - 42.5
3d = 12
d = 4
Thus price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25
