See description-word problem

Question

Store sells 7 coats & 12 umbrellas for $399.45. Later they sell 3 coats & 25 umbrellas for $503.80. If all coats are the same price, and all umbrellas are the same price, what is the price of 1 coat?

Answer 1

Let C=cost of a coat and U the cost of an umbrella.

 

7C + 12U = 399.45

3C + 25U = 503.80

 

There is no easy way to solve this problem...it is messy no matter what way you chose and it is more likely that you will screw up the arithmetic than get stuck on the algebra!  The most direct way, probably, is by determinants which you have probably not yet studied; if you know determinants, then do the problem with that method.

 

Otherwise, brute force multiplication:

Multiply the first equation by 3 and the second equation by 7.

This will allow you to eliminate the C by subtraction and give you an equation involving only U.

Solve the equation for U and plug back into either initial equation to get C.

 

Obviously, I am leaving the arithmetic to you.  Good luck!