A 100% concentrate is to be mixed with a mixture having a concentration of 42% to obtain 53 gallons of a mixture with a concentration of 71%. How much of the 10

Question

A 100% concentrate is to be mixed with a mixture having a concentration of 42% to obtain 53 gallons of a mixture with a concentration of 71%. How much of the 100% concentrate will be needed?

Answer 1

Hi Araceli,

 

Let's begin by assigning a letter to represent our unknown:

    x = number of gallons of 100% concentrate

 

Now let's write an equation using the  numerical information given in the problem and our unknown (x) to express the mixing of the two concentrates giving our final mixture's concentration:

    100% Concentrate = (1.00)(x)

      42% Concentrate = (0.42)(53)

      71% Concentrate = (0.71)(x + 53)

    (1.00)(x) + (0.42)(53) = (0.71)(x + 53)

 

Now let's solve this equation for our unknown (x):

    (1.00)(x) + (0.42)(53) = (0.71)(x + 53)

    x + 22.26 = 0.71x + (0.71)(53)

    x + 22.26 = 0.71x + 37.63

    x - 0.71x = 37.63 - 22.26

    0.29x = 15.37

          x = 15.37 / 0.29

          x = 53 (number of gallons of

                     100% concentrate)

 

We can verify our answer by plugging it back into our equation and checking to see that both sides are equal:

    (1.00)(x) + (0.42)(53) = (0.71)(x + 53)

    (1.00)(53) + (0.42)(53) = (0.71)(53 + 53)

    53.00 + 22.26 = (0.71)(106)

                75.26 = 75.26 (both sides are equal)

 

Since both sides are equal, we are confident that our answer is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.