Answer: soda costs $3
Lemonade costs $4
Water costs $2
Step-by-step explanation:
The table shows the number of Soda, lemonade and water bought by Juan, Lee and morris and the total amount each of them spent in buying these drinks
Juan spent $43 on 5 bottles of soda, 4 bottles of lemonade and 6 bottles of water
Lee spent $34 on 2 bottles of soda, 5 bottles of lemonade and 4 bottles of water
Morris spent $41 on 3 bottles of soda, 7 bottles of lemonade and 2 bottles of water
Let price of soda be x
Let price of lemonade be y
Let price of water be z
From the table
5x + 4y + 6z = 43 - - - - - - 1
2x + 5y + 4z = 34 - - - - - - 2
3x + 7y + 2z = 41 - - - - - - -3
Multiply equation 1 by 2 and equation 2 by 5
10x + 8y + 12z = 86
10x + 25y+20z =170
Subtracting
-17y -8z= -84 - - - - - -4
Multiply equation 2 by 3 and equation 3 by 2
6x + 15y+12z = 102
6x + 14y + 4z = 82
Subtracting
y + 8z = 20 - - - - - 5
Add equation 4 and equation 5
-16y = -64
y= -64/-16 = 4
Put y= 4 in equation 4
-17 × 4 -8z = - 84
-68-8z = -84
-8z = -16
z = -16/-8 = 2
Put y = 4 and z = 2 in equation 1
5x + 4×4 + 6×2 = 43
5x + 16 + 12 = 43
5x = 43-28= 15
x = 15/5 = 3
