Answer:
Cost of each popcorn = $3.50
Cost of drinks = $31.50
Step-by-step explanation:
Let each drink's cost be represented by $d
Let each popcorn's cost be represented by $p
5 drinks = 5*d = $5d; 3 tubes of popcorn = 3*p = $3p
4 drinks = 4*d = $4d; 6 tubes of popcorn = 6*p = $6p
// Setting up the system of equations
5d + 3p = 32.50 ...(1)
4d + 6p = 44.00 ...(2)
Multiply equation 1 by 2
10d + 6p = 65.00 ...(3)
4d + 6p = 44.00 ...(2)
Subtract equation 2 from equation 3
10d - 4d + 6p - 6p = 65.00 - 44.00
6d = 21.00
Divide both sides by 6
[tex]\frac{6d}{6}-\frac{21.00}{6}\\ \\d = $3.50[/tex]
Substitute d = 3.5 in equation 2
4*3.50 + 6p = 44.00
14.00 + 6p = 44.00
6p = 44.00 - 14.00
6p = 30.00
Divide both sides by 6
[tex]\frac{6p}{6} = \frac{30.00}{6}\\ \\p = 5.00[/tex]
So, each popcorn costs $5.00
For the drinks. Angie's family got 5 drinks and Jason's family got 4 drinks. So, a total of 9 drinks.
Cost of drinks = $3.50 * 9 = $31.50
