# A group of students bought 10 barbecues and 12 soft drinks at a cost of Php 320.00 another group bought 6 barbecues and 4 soft drinks at a cost of Php 160.00, how much is a single barbecue?

1
by simplyjessy

• Brainly User
2016-02-04T00:21:18+08:00
Cost of each barbecue: x
Cost of each softdrink: y

Group A (Equation A):
10x + 12y = 320

Group B (Equation B):
6x + 4y = 160

Solve the system using Substitution Method:
Equation B:
6x + 4y = 160
4y = 160 - 6x
4y/4 = 160/4 - 6x/4
y = -3x/2 + 40

Substitute -3x/2 + 40 for y in Equation A:
10x + 12 (-3x/2 + 40) = 320
10x -18x + 480 = 320
-8x = 320 - 480
-8x/-8 = -160/-8
x = 20

Substitute 20 for x in y = -3x/2 + 40
y = -3(20)/2 + 40
y = -60/2 + 40
y = -30 + 40
y = 10

Cost of each barbecue: x = Php 20
Cost of each softdrink: y = Php 10

ANSWER:  A single barbecue costs Php20.

Check:
Group A (Equation A):
10x + 12y = 320
10 (20) + 12 (10) = 320
200 + 120 = 320
320 = 320    (True)

Group B (Equation B):
6x + 4y = 160
6 (20) + 4 (10) = 160
120 + 40 = 160
160 = 160   (True)