could you help me with this math homewok?

Question

okey dokey. to ge 1000 gallons of mixture that was 35.2% alcohol, it was necessary to mix some 20% alcohol solution with some 40% alcohol solution. how much of each solution was required?

(now, i know u use like Pn and Dn and that but i'm just not sure of the rest...could u help me?)

Answer 1

20%(x) + 40%(1000-x) = 35.2%(1000)
let's use decimals and not %'s
0.20x + 0.40(1000-x) = 0.352(1000) = 352
0.20x + 400 - 0.40x = 352
rearrange to get
(400-352) = (0.40 - 0.20)x
48 = 0.20x
x = 240
Check it
0.20(240)+0.4(1000-240) = 352
48 + 0.40(760) = 352
48 + 304 = 352 Woah how about that!

Answer 2

Well, for starters... If you mixed 500 gallons of 20% and 500 gallons of 40%, you'd get 1000 gallons of 30%. So, it must be more than 500 gallons of 40% and less than 500 gallons of 20%.

How do you know this? There are 500 gallons X 0.20 (which is 20% mathematically) = 100 gallons of alcohol in the first 500 gallons. There are 500 gallons X 0.40 (or 40%) = 200 gallons of alcohol in the second 500 gallons. That gives you a total of 300 gallons of alcohol in 1000 gallons of solution, or 300/1000 = 30% alcohol.

What if you mixed 750 gallons of 40% and 250 gallons of 20%? That would get you close - you'd end up with 1000 gallons of 35%. Same math: 750 X 0.40 = 300 gallons of alcohol in the first 750 gallons. 250 X 0.20 = 50 gallons of alcohol in the second 250 gallons. Total alcohol = 350 gallons in 1000 gallons of solution or 350/1000 = 35%.

This is clearly not the way you're supposed to answer the question. I'm sure you've got some kind of formula that does this thinking for you. But sometimes it helps to recognize that there are several ways to get to your answer. A slight adjustment to the second answer I've suggested will get you to the required 35.2%, but I'll let you figure that part out.

Answer 3

Suppose we need x gallons of 20% alcohol and y gallons of 40% alcohol. to make 35.2 % alcohol.
For 20% alcohol:
Quantity of alcohol in it = 0.20x and
Quantity of water in it =0.80x
For 40% alcohol:
Quantity of alcohol in it = 0.40y and
Quantity of water in it =0.60 y
For 35.2% alcohol mixture which is 1000 gallons
Quantity of alcohol in it = 352 gallons and
Quantity of water in it =648 gallons
So: 0.20x + 0.40 y = 352 and
0.80x + 0.60 y =648 These equations can be written as: x + 2y =1760 and
4x +3 y = 3240
Solving these equations, we get x=240 gallons and y=760 gallons. Answer.

Answer 4

Set up a system of eqns:

x=20%
y=40%

x+y=1000
20x+40y=35200

Now just solve for x and y.

You should get:
x=240
y=760

Answer 5

ok, so there's a sq. backyard with an component of two hundred sq. meters. that signifies that both facet is about 14 meters because the sq. root of two hundred is about 14.142... so, imagine a sq. with aspects 14 meters. now draw the diagonal. the left and bottom aspects of the sq. are the LEGS. the diagonal is the HYPOTENUSE. using the pythagorean theorem [a^2 + b^2 = c^2 or leg squared + leg squared = hypotenuse squared], you get 14^2 + 14^2 = c^2 then, 392 = c^2 and also you sq. root both facet to get c. c = about 20 meters so, the hypotenuse is about 20 meters. good success! =]

Answer 6

What are Pn and Dn?

0.2x + 0.4y = 0.352*1,000
x + y = 1,000
0.2x + 0.2y = 0.2*1,000
0.2y = 0.152*1,000
y = 760 gal.
x = 240 gal

Answer 7

SAy What?wheres the answer?

Answer 8

no