Kim sells pistachio pleasure containing 80% pistachio nuts and pistachio surprise containing 30% pistachio nuts how much of each 12 pound of a new mix that is 40% pistachio nuts

p = pounds of pistachio pleasure

s = pounds of pistachio surprise

Kim wants a new mixture weighing 12 pounds:

p + s = 12

A pound of pleasure contains 0.8 pound of pistachios, and a pound of surprise contains 0.3 pound of pistachios. Each pound of the new mixture should contain 0.4 pound of pistachios, so the mix should contain 0.4 • 12 = 4.8 pounds:

0.8p + 0.3s = 4.8

Solve the system:

s = 12 - p

0.8p + 0.3(12 - p) = 4.8

0.8p + 3.6 - 0.3p = 4.8

0.5p = 1.2

p = 2.4

s = 12 - 2.4

s = 9.6

step-by-step explanation:

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(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