Please Help! I'm so confused

Question

Maria is going to the store to buy candles. Small candles cost $3.50 and large candles cost $5.00. she needs to buy at least 20 candles and she cannot spend more than $80.

  Write a system of linear inequalities, and give two combinations of candles she can buy.

Answer 1

Cost ( x , y) =  3.50x + 5y  where x is the number of small candles and y is the number of large candles

 

x+y >=20 

 

Cost(x,y)<=80

 

y >= 20 - x

 

-------------------------

 

y = 20 -x   vs.  80 = 3.5x + 5y

 

             80 = 3.5x + 5( 20 - x)

             80 = 3.5x + 100 - 5x

 

             80 = 100 - 1.5x

 

             -20 = -1.5x

 

              -200 = -15x

 

              x = 200/15 = 40/3

 

          y = 20 - 40/3 = 20 = 13 and 1/3 = 6 and 2/3

 

  THe lines intersect at ( 13 and 1/3 , 6 and 2/3)

 

  (40/3)*3.5 + 5 * (20/3) = (40/3)(7/2) + 5 * (20/3) = 280/6 + 100/3 = 280/6 + 200/6 = 480/6 = 80

 

  So 13 and 1/3 small candles and 6 and 2/3 large candles costs exactly $80

 

She can buy 14 small candles and 6 large candles for $79

 

She can buy 15 small candles and 5 large candles for  $77.50

 

She can buy 16 small candles and 4 large candles for $76

 

She can buy 17 small candles and 3 large candles for $74.50

 

She can buy 18 small candles and 2 large candles for $73

 

She can buy 19 small candles and 1 large candles for $71.50

 

She can buy 20 small candles for $70