Drawing Flowers Draw A Rose
Math Story Poblem, I am not very good at these and need help with a starting point, please!?
Here is the problem: A modernistic painting consists of triangles, rectangles & pentagons, all drawn so as to not overlap or share sides. Within each rectangle are drawn 2 red roses & each pentagon contains 5 carnations. How many triangles, rectangles & pentagons appear in the painting if the painting contains a total of 40 geometric figures,153 sides of geometric figures and 72 flowers?
How do I set this up so that I can solve it? I am sure if I can get it set up that I can solve it! Can you help me?
Thanks in advance,
Jennifer
That is a ridiculous problem, but this is how you do it. Set up a system. Let x be the triangles, y be the rectangles, and z be the pentagons.
So, now you start setting up equations to use what you know. 3x+4y+5z=153 (this models the sides of the figures)
x+y+z=40 (modelling that there are 40 shapes together)
2y+5z= 72 models the number of flowers. there is no x term, because there was no info given concerning the flowers in a triangle.
So, to solve the system, use graphing, or substitution – whatever method you know best….
Here is using substitution:
x=40-y-z
3(40-y-z)+4y+5z=153
Distribute: 120-3y-3z+4y+5z=153
Simp: y+2z=33
y=33-2z
Put that into the equation that only has y and z…..
2(33-2z)+5z=72
z=6
So, x+y+6=40
x+y=34
x=34-y
Sub that in to the first eq, and you end up with z=6, y=21and x=13…..
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