SOLUTION: A woman decided to bake fruit cakes and sponge cakes.she has only 2kg flour and 1,2kg sugar.she has and abundance of all the other ingredients.for a fruit cake she needs 500g flour

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A woman decided to bake fruit cakes and sponge cakes.she has only 2kg flour and 1,2kg sugar.she has and abundance of all the other ingredients.for a fruit cake she needs 500g flour      Log On


   

Question 715070: A woman decided to bake fruit cakes and sponge cakes.she has only 2kg flour and 1,2kg sugar.she has and abundance of all the other ingredients.for a fruit cake she needs 500g flour and 100g sugar.for a sponge cake she will use 200g flour and 200g sugar.she would like to bake at least 5 cakes
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
(Note, the graph below shows lines but no inequalities shading)
Letting x be how many fruit cakes and y be how many sponge cakes, and all measures as kilograms, here's an accounting for flour and sugar quantities:

Which cake_____________flour_________________sugar
Fruit Cake___________0.5x____________________0.1x
Sponge Cake__________0.2y____________________0.2y
Total Materials____0.5x+0.2y______________0.1x+0.2y

The Required Cakes Inequality:
x+y>=5, gives us y%3E=-x%2B5

Flour Sum Inequality:
0.2y%3C=2-0.5x
y%3C=%282%2F0.2%29-%28.5%2F.2%29x
y%3C=-%285%2F2%29x%2B10

The Sugar Sum Inequality:
0.2y%3C=-0.1x%2B1.2
y%3C=-%281%2F2%29x%2B1.2%2F0.2
y%3C=-%281%2F2%29x%2B6

Summary of the Inequalities:
highlight%28y%3E=-x%2B5%29
highlight%28y%3C=-%285%2F2%29x%2B10%29
highlight%28y%3C=-%281%2F2%29x%2B6%29
Graphing those and shading the proper regions seem to point out x=1 fruit cake and y=4 sponge cakes. Another possiblility is 3 fruit cake and 3 sponge cake. Or another way to use the flour and sugar is 5 or 6 sponge cakes but none of any fruit cakes. A few other answers are found in the graph.
I present here the graph alone without any shading for inequalities: