SOLUTION: A painter has exactly 32 units of yellow dye and 54 units of green dye. he plans to mix as many gallons as possible of color a and color b. each gallon of color a requires 4 units

Question 517190: A painter has exactly 32 units of yellow dye and 54 units of green dye. he plans to mix as many gallons as possible of color a and color b. each gallon of color a requires 4 units of yellow dye and 1 unit of green dye. Each gallon of color b requires 1 unit of yellow dye and 6 units of green dye. find the maximum number of gallons possible.
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 green dye.
he plans to mix as many gallons as possible of color a and color b.
each gallon of color a requires 4 units of yellow dye and 1 unit of green dye.
Each gallon of color b requires 1 unit of yellow dye and 6 units of green dye. find the maximum number of gallons possible.
:
Write a total yellow units equation
4a + 1b = 32
:
Write a total green units equation
1a + 6b = 54
:
Use the 1st equation for substitution in the 2nd equation
4a + 1b = 32
1b = (32-4a)
replace b with (32-4a) in the green equation
1a + 6(32-4a) = 54
1a + 192 - 24a = 54
1a - 24a = 54 - 192
-23a = -138
a =
a = 6 gal of color a
then
32 - 4(6) = 8 gal of color b
:
:
Let's see if that checks out
Yellow: 6(4) + 8(1) = 32 units of yellow used
Green: 6(1) + 8(6) = 54 units of green
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