How many liters each of a 45% acid solution and a 75% acid solution must be used to produce 60 liters of a 70% acid solution? (round to two decimal places if necessary)

Question

anonymous · Answer

x+y=60
.45x+.75y=60(.70)

amistre64 · Answer

a + b = t
a = t-b

a(x) + b(y) = t(z)

(t-b)(x) + b(y) = t(z)

tx -bx +by = tz

b(y-x) = t(z-x)

b = t(z-x)
       -----
        (y-x)

b = 60(.70-.45)  at 45%
       ----------
          (.45-.75)

amistre64 · Answer

got my numbers backwards on the bottom :)

b = 60(.70-.45) at 45% 
      ---------- 
        (.75-.45)

amistre64 · Answer

50 at 75% ... seems better; still new at it :)

anonymous · Answer

and then 10 at 75%?

amistre64 · Answer

yes; but (50) at 75% and (10) at 45%