SOLUTION: A painter has exactly 32 units of yellow dye and 54 units of blue dye. She plans to mix the dyes to make two shades of green. Each gallon of the lighter shade of green requires 4

Question 119159This question is from textbook Algebra 1
: A painter has exactly 32 units of yellow dye and 54 units of blue dye. She plans to mix the dyes to make two shades of green. Each gallon of the lighter shade of green requires 4 units of yellow dye and 1 unit of blue dye. Each gallon of the darker shade of green requires 1 unit of yellow dye and 6 units of blue dye.
29. Make a graph showing the numbers of gallons of the two greens she can make.
30. List three possible solutions. This question is from textbook Algebra 1

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A painter has exactly 32 units of yellow dye and 54 units of blue dye. She plans to mix the dyes to make two shades of green. Each gallon of the lighter shade of green requires 4 units of yellow dye and 1 unit of blue dye. Each gallon of the darker shade of green requires 1 unit of yellow dye and 6 units of blue dye.
:
Let x = gallons of the light green
Let y = gallons of the dark green
:
Yelo dye eq: 4x + 1y = 32
Blue dye eq: 1x + 6y = 54
:
29. Make a graph showing the numbers of gallons of the two greens she can make.
Arrange the two equations for graphing and plot x: 0 to +12; y: 0 to +16
:
y =-4x+32: purple line on the graph
and
6y = -x + 54
y = --
y = -+ 9 ; green line
:

:
:
30. List three possible solutions.
:
1.The point of intersection; x=6,y=8;
6 gal light green, 8 gal dark green
:
2. x=8;y=0;
8 gal of light green, 0 gal of dark green
:
3. x=0;y=9;
9 gal of dark green, 0 gal of light green
:
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