Question

Juan and his friends bought drinks for a charity event. The table shows the numbers of each kind of drink bought, and the amount each person spent. Identify the price of each kind of drink. HELP PLEASE!!

Answer 1

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