Achemical company makes two brands of antifreeze. the first brand is 70% pure antifreeze, and the second brand is 85% pure antifreeze. in order to obtain 150 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?

50 gallos of 70%

100 gallons of 85%

Step-by-step explanation:

x = amount of 70% antifreeze

y = amount of 85% antifreeze 

   EQUATION 1:   x + y = 150    (total of 150 gallons mixed) 

   EQUATION 2:  .70x + .85y = .80(x + y)

    Multiply second equation by 100 on both sides to remove the decimals           70x + 85y = 80(x + y)  

  70x + 85y = 80x + 80y   (distributive)     

  70x - 80x + 85y - 80y = 0          

 -10x + 5y = 0      

Now we have the following system of equations:        

     x  +  y = 150     

  -10x +5 y = 0  

 Multiply the first equation by 10 to get opposite coefficients for x;  add the equations to eliminate x        

  10x + 10y = 1500       

 -10x + 5y =       0     

                15y = 1500    

 Solve for y            15y = 1500                y = 100

x+100=150    x=50

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following