Angie's family goes to the movies and got popcorn and drinks to enjoy during the show. The family got 5 drinks and 3 tubes of popcorn to share. They spent $32.50 on concessions. JASON FAMILY GOT 4 DRINKS AND 6 TUBES OF POPCORN TO SHARE. THEY SPENT $44.00. HOW MUCH DID EACH POPCORN COST AND HOW MUCH WHERE DRINKS?

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

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

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

tickets for the harlem globetrotters

show at michigan state university in

2010 cost $16, $23, or, for vip seats, $40.

total revenue = 16x + 23y + 40z

if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, sales of all three kinds of tickets would

total $46,575.

16x + 23y + 40z = 46575, how many of each kind of ticket would

have been sold?

solve for x, y and z

x − 9z = 0

x − y − z = 55

16x + 23y + 40z = 46575

x = 1170

y = 985

z = 130

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step-by-step explanation: