How much does one coat cost?

Question

On Monday a store sells 7 coats and 12 umbrellas for $399.45 and on Tuesday the store sells 3 coats and 25 umbrellas for $503.80. All coats cost the same and all umbrellas cost the same.

Answer 1

Let x = cost of coat and y = cost of umbrella

 

On monday, 7 coats and 12 umbrellas were sold for a total of 399.45:

 

7x + 12y = 399.45 eq.1

 

On tuesday, 3 coats and 25 umbrellas were sold for a total of 503.8:

 

3x + 25y = 503.8 eq.2

________________________

 

Through elimination:

 

Multiply eq.1 by 3 and eq.2 by 7, you'll get:

 

21x + 36y = 1198.35

21x + 175y = 3526.6

 

Subtracting the two:

 

-139y = -2328.25

 

y = 16.75

 

Using any equation:

 

3x + 25(16.75) = 503.8

 

x = $28.35