6. Ruth is having hardwood floors installed in her living room. The cost for the material is $2840 plus an installation charge of $1.90 per square foot. If the total cost for the material plus installation is $5120, determine the area of her living room. 7. Sean is deciding whether to select a satellite receiver or cable for his television programming. The satellite receiver costs $298.90 and the monthly charge is $68.70. With cable, there is no initial cost to purchase equipment, but the monthly charge for comparable channels is $74.80. After how many months will the total cost of the two systems be equal

Let the area of the living room be x square feet. Since the material cost is fixed as $2840 and cost ler square feet provided as $1.9 while and the total cost is given as $5120 then the the problem can be represented as

1.9x+$2840=$5120

Putting like terms together then

1.9x=$5120-$2840=$2280

Making x the subject of the above, by dividing both sides by 1.9 then

X=2280/1.9=1200 square feet.

Therefore, area is 1200 square feet.

(7)

Let the number of months when cost are similar be y.

For satelite option, since fixed cost of $298.9 is charged then monthly rate is $68.7 it means after y months, the expenditure for this plan will be 68.7y+$298.9

For cable option, since it only charges monthly fee of $74.80 then after y months, the expenditure amounts to 74.80y

Since after y months the expenses are same, then we equate both options to be equal. Therefore,

74.80y=68.70y+298.90

Putting like terms together then

74.80y-68.70y=298.90

6.1y=298.90

Dividing both sides by 6.1 to make y the subject then

Y=298.9/6.1=49 months