19 an artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. the mosaic must be at least 3 feet tall and 5 feet wide. the tiles in the mosaic have words written on them and the artist wants the words to all be horizontal in the final mosaic. the word tiles come in two sizes: the smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. if the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? what is the minimum cost?

Total tiles need - 30 large tiles and 0 small tiles

Minimum cost is $135

Step-by-step explanation:

Allow dimensions are

Smallest allowed dimensions are    

2 things need to be noticed

   1. smaller thee total size of final mosaic, cheaper the cost

   2.  Greater thee number of large tiles, cheaper the mosaic

   Place   to fully cover the size of rectangle

                       and

.

Therefore,total tiles need

 (& 0 small tiles).

The minimal cost is  

7

step-by-step explanation:

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.