Question

Rex mixed x liters of fruit syrup with y liters of water to make a fruit punch. Three times the number of liters of water he mixed was 6 more than twice the number of liters of syrup he mixed. The total number of liters of syrup and water he mixed was 7 liters. Which graph best shows the number of liters of fruit syrup and water that Rex added to make the fruit punch?

Answer 1

the solution is (3,4) (the second one)

Explanation:

Answer 2

The correct graph is attached to the answer.

The amount of fruit syrup Rex added is: 3 liters

and the amount of water he added is: 4 liters.

Explanation:

x denote the amount of fruit syrup added and y denote the amount of water added.

It is given that:

Three times the number of liters of water he mixed was 6 more than twice the number of liters of syrup he mixed.

i.e. the equation that satisfies this condition is:

`3y=2x+6\\\\i.e.\\\\2x-3y=-6-----------(1)`

i.e. the graph of this equation is a line that passes through (-3,0) and (0,2)

Also, The total number of liters of syrup and water he mixed was 7 liters.

Hence, the equation is:

`x+y=7------------(2)`

i.e. the graph of this equality is a line that passes through (7,0) and (0,7)

Also, from equation (2) we have:

`x=7-y`

Now, on putting this value of x in terms of y in equation (1) we get:

`2(7-y)-3y=-6\\\\i.e.\\\\14-2y-3y=-6\\\\i.e.\\\\14-5y=-6\\\\i.e.\\\\14+6=5y\\\\i.e.\\\\5y=20\\\\i.e.\\\\y=4`

Also, on putting the value of y in equation (2) we get:

`x=3`

Hence, the solution to the system of linear equation is:

(3,4)