Luke is having a rectangular swimming pool built in his back yard. he wants it to be 30 feet longer than it is wide. he also has to
decide how deep he wants the pool to be. he wants the width of the pool to be at least 15 feet greater than the depth.
the cost of the pool will be based on the depth and area of the pool. the cost of the pool will be $10 per square foot of perimeter
plus $30 per foot of depth. luke can afford to spend no more than $15,000 on the construction of the pool.
create a sustem of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

list

6,24,51,72,12,54,80,44,57,64,92,26,66,96

your welcome!