1 lbs of candy 1: $1.05 | 1lbs of candy 2: $1.35 | candy 1 + candy 2 create worth $1.17 a lbs. | how many lbs of each candy were used to make 30 lbs

Question

Please include all steps. I am very confused. Thank you for your time

Answer 1

Let X = lbs of candy 1

Let Y = lbs of candy 2

 

30 lbs total  ==>  X + Y = 30  ==>  X = 30 - Y

 

The total cost of 30 lbs candy at 1.17 a lbs is 30 * 1.17 = 35.10  

 

The total cost of X pounds of candy 1 and Y pounds of candy 2 is 

 

1.05*X + 1.35*Y

 

So our 2nd equation is 1.05*X + 1.35*Y = 35.10 

 

Substitute the value for X above in to this equation 

 

1.05*(30-Y) + 1.35*Y = 35.10

31.50 - 1.05*Y + 1.35*Y = 35.10

0.30*Y = 3.60

Y = 3.60 / 0.30 = 12

 

So X = 30 - 12 = 18 

 

18 lbs of candy 1 and 12 lbs of candy 2 were used.  

 

Check :  18 + 12 = 30 lbs total 

             1.05*(18) + 1.35*(12) = 18.90 +16.20 = 35.10 

             which is 35.10 / 30 = $1.17 a lbs