first, define ur variables.
let x equal the price of the medium drink
let y equal the price of the large popcorn
let’s start by creating an equation for the couple
they bought 2 drinks and 1 popcorn for 13.85$
so, 2x+1y=13.85
let’s make an equation for the family
they bought 3 drinks and 2 popcorns for 23.90$
so, 3x+2y=23.90
let’s solve for y using the COUPLE equation
minus 2x from the right to get 1y=-2x+13.85
1y is the same as y, the the equation for the couple is y=-2x+13.85
put this y value into the y value for the FAMILY equation
3x+2(-2x+13.85)=23.90
distribute the 2 to get 3x-4x+27.70=23.90
combine 3x and -4x to get -1x+27.70=23.90
minus 27.70 from both sides to get the following:
-1x=-3.8
multiple both sides by -1 to get x=3.8
the price of one drink is 3.8$
lastly, let’s figure out the price of the popcorn.
replace the x value in the COUPLE equation with the 3.8
2(3.8)+1y=13.85
multiply 2 and 3.8 to get 7.6
7.6+1y=13.85
minus the 7.6 to get 1y=13.85-7.6
reduce the equation to get y=6.25
so, the price of one drink is 3.80$ and one popcorn is 6.25$
hope this helped!!