The miller family visited mama's kitchen and ordered 4 hamburgers and 3 medium fries and paid $15.24. james ordered a medium drink, a hamburger, and 2 medium fries and paid $6.53. steven ordered 2 hamburgers, medium fries, and a medium drink for $8.17. how much did each item cost?

4h + 3f = 15.24
h + 2f + d = 6.53
2h + f + d = 8.17

h + 2f + d = 6.53multiply by -1
2h + f + d = 8.17

-h - 2f - d = - 6.53 (result of multiplying by -1
2h + f + d = 8.17
add
h - f = 1.64

h - f = 1.64...multiply by -4
4h + 3f = 15.24

-4h + 4f = - 6.56 (result of multiplying by -4
4h + 3f = 15.24
add
7f = 8.68
f = 8.68/7
f = 1.24 <fries cost 1.24

h - f = 1.64
h - 1.24 = 1.64
h = 1.64 + 1.24
h = 2.88 < hamburgers cost 2.88

h + 2f + d = 6.53
2.88 + 2(1.24) + d = 6.53
2.88 + 2.48 + d = 6.53
5.36 + d = 6.53
d = 6.53 - 5.36
d = 1.17 <=== 1.17 for the drinks

(24, 224 ) i.e. 24 basketball and 224 footballs

Step-by-step explanation:

Basketball :

uses 4 ounces of foam

20 minutes of labor

profit = $2.50

Football :

uses 3 ounces of foam

30 minutes of labor

profit = $2

Manufacturer has :

768 ounces of foam , 120 labor hours per week,

using the simplex method to determine the optimal production schedule so as to maximize profits

lets assume

x = number of basketball

y = number of footballs

maximize = 2.5 x + 2y  from a linear programming problem

attached below is the detailed solution