A solution of 51% pesticide is to be mixed with a solution of 35% pesticide to form 144 liters of a 42% solution. How many liters of the 51% solution must be used?
[a] 63 liters
[b] 73 liters
[c] 120 liters
[d] 119 liters
please show me how to do it
thanks :)
2007-10-29 16:49:47 · 4 answers · asked by vennysweetgirl21 3 in Science & Mathematics ➔ Mathematics
percent1 x amount1 + percent2 x amount2 = percent3 x (amount1 + amount2)
51%(x) + 35%(144-x) = 42%(144)
51x + 35(144) - 35x = 42(144)
51x - 35x = 42(144) - 35(144)
16x = 7(144)
x = 63 L
2007-10-29 17:09:24 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
Let A = amount of 51% pesticide
Let B = amount of 35% pesticide
We know that : A+ B = 144L of diluted pesticide
and .51A + .35B = .42(144) L of pure pesticide
144 x .42 = 60.48, so
.51A + .35B = 60.48 L of pure pesticide
We change first known formula by saying A+ B = 144 so A = 144 - B, and substitute that formula into second known formula and you have...
.51(144 - B) + .35B =60.48
simplify to remove the brackets... (0.51 x 144 = 73.44) so
73.44 - .51B + .35B = 60.48
simplify by combining the two expressions with B
73.44 - .16B = 60.48
move 73.44 to the other side of the equation
- .16B = 60.48- 73.44
simplify the right side
- .16B = -12.96
divide both sides by - .16
B = 81
Therefore, there are 81 L of the 35% solution, which leaves 63 L of the 51% solution (according to the first known formula A+B = 144 L) . Answer A is correct. I solved for B rather than A. Try doing the problem yourself, solving for A instead of for B, and see if you can get the correct answer that way.
2007-10-30 00:27:40 · answer #2 · answered by Norm D 2 · 0⤊ 0⤋
x = qty of 51%
y = qty of 35%
x + y = 144
y = 144 - x
The mix
51x + 35(144 - x) = 42(144)
solve for x
51x + 5040 - 35x = 6048
16x = 1008
x = 63
2007-10-30 00:04:31 · answer #3 · answered by kindricko 7 · 0⤊ 0⤋
this is hurting my head...
2007-10-29 23:55:10 · answer #4 · answered by nquanghn 2 · 0⤊ 1⤋