Trisha uses 3 cups of sugar for every 2 teaspoons of baking soda to make a batch of cookies. Which equation should she use to find the number of teaspoons of baking soda, x, needed if she uses 9 cups of sugar?

Given:

Trisha uses 3 cups of sugar for every 2 teaspoons of baking soda to make a batch of cookies.

To find:

The equation that she should use to find the number of teaspoons of baking soda, x, needed if she uses 9 cups of sugar.

Solution:

Let the number of teaspoons of baking soda be x, that is needed if she uses 9 cups of sugar.

For every 2 teaspoons of baking soda Trisha uses 3 cups of sugar.

For every 1 teaspoons of baking soda Trisha uses cups of sugar.

For every x teaspoons of baking soda Trisha uses cups of sugar.

Since she uses 9 cups of sugar for every x teaspoons of baking soda, therefore,

Multiply both sides by 2.

Divide both sides by 3.

Therefore, the required equation is and the number of required teaspoons of baking soda is 6.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3