number/cost word problem

Question

I'm doing this out of a textbook that gives me the answer as $40 but gives no explanation as to why and none of the other examples of number word problems have anything remotely similar to this problem: 

 

A green flag costs 10 times the price of a blue flag. A red flag costs half as much as a green flag. An orange flag costs $10 less than a red flag. If all four different colors of flags cost a total of $200, what is the cost of the orange flag?

Answer 1

b = cost of blue flag

10b = cost of green flag

5b = cost of red flag  (half of a green flag)

5b - 10 = cost of orange  (10 less than red flag)

 

b + 10b + 5b + 5b - 10 = 200

21b - 10 = 200

21b = 210

b = 10

 

5b - 10 = 40

Answer 2

What you have to do for this problem is set up a series of equations...

From these sentences, we can convert them into equations:

"A green flag costs 10 times the price of a blue flag" - g=10b

"A red flag costs half as much as a green flag" - r=(1/2)g

"An orange flag costs $10 less than a red flag" - o=r-10

"all four different colors of flags cost a total of $200" - g+b+r+o = 200

 

There are multiple different ways to solve this. One of the easiest methods (if you know how to set it up) is by using a matrix and reducing it to Reduced Row Echelon Form.

Another way that you can solve this (and the way I am going to) is by back-substitution and solve for individual variables.

g=10b

r=(1/2)g=(1/2)*10b=5b

o=r-10 = 5b-10

g+b+r+o=200

10b+b+5b+(5b-10)=200

21b-10=200

21b=210

b= 10

g= 10b = 100
r= 5b = 50
o= 5b-10 = 40

 

Hope this helps,

Chris