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 %26amp; pentagons, all drawn so as to not overlap or share sides. Within each rectangle are drawn 2 red roses %26amp; each pentagon contains 5 carnations. How many triangles, rectangles %26amp; 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

Math Story Poblem, I am not very good at these and need help with a starting point, please!?
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.....
Reply:Ultimately, we have to find the number of triangles, rectangles, and pentagons. So let those be our variables. Let T, R, and P, be the number of triangles, rectangles, and pentagons, respectively.



We're told that the painting has 40 shapes in total, so

T + R + P = 40.



We're also told that there are "153 sides of geometric figures". There are three sides on a triangle, 4 on a rectangle, and 5 on a pentagon. So the total number of sides must be the number of sides from triangles (3T), plus the number of sides from rectangles (4R), plus the number of sides from pentagons (5P). This means:

3T + 4R + 5P.



Finally, we're told that there are 72 flowers in total. There are 2 roses in each rectangle and 5 carnations in each pentagon. We're not told how many are in the triangles, so we'll just assume there aren't any in them. This means:

2R + 5P = 72.



You now have 3 equations with 3 unknowns. Solve using substitution.