Problema Solution
Brand A antifreeze is 85% ethylene glycol. Brand B is 60% ethylene glycol. The two brands are to be mixed.
A. Define variables for the number of gallons of each kind used. Then write an expression for the number of gallons of ethylene glycol in the mixture.
B. If 100 gallon of brand A is mixed with 150 gallons of brand B find:
i. the number of gallons of ethylene glycol in the mixture;
ii. the percent of ethylene glycol in the mixture;
C.If 1000 gallons of the mixture is to have 78% ethylene glycol, how many gallons of each brand should be used?
Answer provided by our tutors
A. Define variables for the number of gallons of each kind used. Then write an expression for the number of gallons of ethylene glycol in the mixture.
let
a = gal of brand A
b = gal of brand B
the number of gal of ethylene glycol in the mixture is:
0.85a + 0.60b
B. If 100 gallon of brand A is mixed with 150 gallons of brand B find:
i. the number of gallons of ethylene glycol in the mixture;
a = 100 gal
b = 150 gal
0.85*100 + 0.60*150 = 175 gal of ethylene glycol
ii. the percent of ethylene glycol in the mixture;
(175/(100 + 150))*100 = 70%
C.If 1000 gallons of the mixture is to have 78% ethylene glycol, how many gallons of each brand should be used
0.85a + 0.60b = 0.78*1000
a + b = 1000
by solving the above system of equations we find:
a = 720 gal
b = 280 gal
click here to see the step by step solution of the system of equations:
720 gal of brand A and 280 gal of bran B should be used.