<ol>
<li><p>How many quarts of cream containing 36% butterfat must be added to 100 quarts of milk containing 3% butterfat to produce 4% milk?</p></li>
<li><p>An automobile radiator contains 12 quarts of a 20% antifreeze and water solution. How much must be replaced by 80% antifreeze to make a 30% solution?</p></li>
<li><p>Al invested $10,000 in two savings accounts, one that paid 4% and the other 5%. If his total earnings in one year was $480, then how much was invested at each rate?</p></li>
</ol>
<p>The answers I got: 1) 2.778 qt. of cream 2) 2.4 qt. of 80% antifreeze sol. 3) $2,000 in 4% account, and $8,000 in 5% account</p>
<ol>
<li><p>One hour and 20 minutes after a hiker started down a mountain trail a ranger started after him on horseback and overtook him in 40 minutes. Find the speed of each if the ranger rode 6 miles per hour faster than the man walked.</p></li>
<li><p>A lady drove to a city 30 miles away to shop and returned home in the evening. She spent 15 minutes longer driving the return trip than in the going, and she drove three-fourths as fast when returning as she did when going to the city. How long did it take her to drive to the city?</p></li>
</ol>
<p>Are the answers: 4) hiker: 3 mph, ranger: 9 mph 5) 45 min to drive to city ?</p>
<p>6.A boy could spade his garden in 6 hours, while his father could spade it in 4 hours. How long would it take the two working together to spade the garden?</p>
<p>7.It takes Ashley three times as long to paint a room as it does Aaron. Working together, they can paint the room in 6 hours. How long would it take Aaron to paint the room by himself?</p>
<p>8.A laboratory instructor can prepare the solutions for a certain chemical demonstration in 1 hour, while his assistant requires 1 ½ hours to prepare the same solutions. After they had worked together for 30 minutes, the instructor had to meet a class and the assistant finished the work. How long did it take him?</p>
<p>Are these answers correct: 6) 2.4 hr 7) 8 hr 8) 15 min ?</p>
<p>Hm, I thought 4% milk would mean 96% butterfat…?</p>
<p>I don’t understand how you made this:
.36(x) +.03(100)=4</p>
<p>So you’re adding up the butter fat presented in each quart and adding it to the butter fat in the 100 quarts… I thought the milk content was supposed to be the 4% not the butter fat according to what you wrote.</p>
<p>And why 4? hm… I thought that everytime you add a quart in, the solution continues to get diluted past 100*.04… My god, I don’t get it lol.</p>
<p>This is the equation i make if you meant to say 4% butterfat.</p>
<p>(3+.36x)(100+x) = .04, which means x = 3.125 quarts. This makes logical sense, when you mutiply it out to get</p>
<p>3+.36x = 4 + .04x, because the amount being added is increasing to and not staying at 100 quarts.</p>
<p>I thought 4, because 4% of 100. So I was thinking x qt. of cream + 100 qt. of milk = 4 qt milk. But how can x and 100 come out to four?! So I think this is wrong.</p>
<p>Maybe eq. should be .36(x) + .03 (100)= .04 (x+100)…still this seems off…</p>
<p>Ah, not yet, but when I have time. This question was getting on my nerves, haha. But really, How can you possibly dilute something down to 4% milk by adding more then 4% milk to it… It’s not even possible logically speaking.</p>
<p>I think the % butterfat is irrelevant.
We have a 100 quarts of milk (which is 100% milk, the butterfat is just a component that makes it milk) and we want to know how much cream to add to to it (which by the way is 0% milk, its a 100% cream!) So we can setup the equation
100=.04(x+100) where x is qt. of cream.
Solving for x we get 2400 qt of cream.
This may be wrong but I think it works =)</p>
<p>Also [100 qt. milk/ 2500 (milk +cream)] is 4% milk</p>
<p>Answer: 2400 qt.s of Cream must be added to produce 4% milk.</p>
<p>^Huh, cream is made out of 64% milk and 36% butter fat I think.</p>
<p>This really goes down to what the cream is made out of honestly… Badly worded question…</p>
<p>Your new thing makes half the information useless in the question which really seems sketchy. Honestly, I really thinks its a typo or something… It should be 4% butterfat, and it works perfectly.</p>
<p>Half the question would be useless if butter fat didn’t mean anything.</p>
<p>Your saying that theres no milk in cream, so you’re just pouring in anything, it could sulfuric acid in fact. And you then claim milk is 100% milk so your just adding some substance in to get the milk to be only 4%… Which is skipping around the question because the milk is made of 3 quarts of butter fat, and 97 quarts of milk, while the cream is made of .64 quarts of milk for each .36 quarts of butter fat.</p>
<p>The original wording is broken too. It’s hard to say loool.</p>
<p>Thanks Grozza!
It helps to see that other people end up with the same answers as me.
Sometimes you just have those days!
Besides I’m glad you actually looked over the problems. Of all the views this thread has you were the first to say anything about problems 2-8!
I hope our answers are correct =)
Oh and what do you think of problem 1?</p>