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5. Suppose you have $15.00 to plant a vegetable garden. If you spend $6.00 on seeds, how many packs of vegetable plants could you buy for $0.75 each? 6. The SGA makes a profit of $126.00 selling bags of popcorn. If their expenses were $22.50, how many $1.50 bags of popcorn did he sell? Use mathematics to justify your answer. 7. The Tiger's basketball team scored 87 points in their 1st game, 68 points in their 2nd game, and 95 points int heir 3rd game. How many points must they score in their 4th game to have an average of 85 points? Use mathematics to justify your answer. 8. Marly bought an iPod shuffle for $85.00 and pays $1.29 per (x) song. - Write a expression to represent the amount of money spent on her iPod shuffle. - How much would it cost to to purchase an iPod and 8 songs? Use mathematics to explain your answer. - If she spends $109.51 on her iPod and some songs, how many songs did she buy? Use mathematics to justify your answer.
What's the four step process?
Step 1: Understand the problem. Sometimes the problem lies in understanding the problem. If you are unclear as to what needs to be solved, then you are probably going to get the wrong results. In order to show an understanding of the problem, you, of course, need to read the problem carefully. Sounds simple enough, but some people jump the gun and try to start solving the problem before they have read the whole problem. Once the problem is read, you need to list all the components and data that are involved. This is where you will be assigning your variable. Step 2: Devise a plan (translate). When you devise a plan (translate), you come up with a way to solve the problem. Setting up an equation, drawing a diagram, and making a chart are all ways that you can go about solving your problem. In this tutorial, we will be setting up equations for each problem. You will translate them just like we did in Tutorial 2: Algebraic Expressions and Tutorial 5: Properties of Real Numbers. Step 3: Carry out the plan (solve). The next step, carry out the plan (solve), is big. This is where you solve the equation you came up with in your 'devise a plan' step. The equations in this tutorial will all be linear equations. If you need help solving them, by all means, go back to Tutorial 7: Linear Equations in One Variable and review that concept. Step 4: Look back (check and interpret). You may be familiar with the expression 'don't look back'. In problem solving it is good to look back (check and interpret).. Basically, check to see if you used all your information and that the answer makes sense. If your answer does check out, make sure that you write your final answer with the correct labeling.
2. Kerri spent $8.00 on lemonade stand and charged $0.50 per lemonade. If she made a profit of $20.00, how many lemonades did Kerri sell? Do we understand this problem?
For me, I understand Having to pay $8 for a lemonade stand, and selling each lemonade for $.50, but profit is a stretch. Same for you?
yes. Would the equation be let s = lemonades 20=8=.5s ?
profit will be the amount you make from lemonades minus the amount the stand costs. The amount you make will depend on how many you sell times the price of each.
Ok, I'm jumping the gun I guess. Understand the problem. Know how the "things that matter"... how much are you selling lemonade for? How much did your stand cost? How much profit did you make? What information do you not know yet that you need to know?
what I put about profit is "devising a plan"
so 20=.5s-8 ?
i got it
That's what I got! We had to understand what profit is to go on! Now we're understanding the problem AND creating and equation :)
So, as long as you understand all that you've done, we can continue to solving.
I understand it
Nice! Have you solved for s yet?
next: 3. A batting cage charges $4.00 for admissions and $3.00 for a bucket of baseballs. If Ed cannot spend more than $16.00, how many buckets of baseballs could he buy?
@jgurl.3958, @theEric is all over this one :) Pay attention... I will too :)
Thank you, @JakeV8 ! Feel free to interject at any time! :)
wait, i got the next one too. so now: 4. Suppose you earn $5.85 per hour working as a part-time dry cleaner. You need to earn $100.00. How many full hours do you need to earn the money? And more.
@jgurl.3958 make sure you provide responses for each of the 4 steps... you seem to be jumping ahead, which is fine if you get the idea and can do the rest on your own, but the point of the exercise is to make you go in an orderly fashion through these tried-and-true steps of problem solving... They want you to do problem solving like they talk about fire drills... "walk calmly to the door and out of the building" NOT like, "hey!! I can jump to safety!! Wheee! (crash)"
you may "see" instantly how to solve these, but the point is that jumping right in can lead to silly errors... follow the steps and you can't miss!
So part-time dry cleaner doesn't really matter... So I understand getting $5.85 per hour; each hour you get $5.85. And I understand getting $100. And we need to understand how to get there. Haha, nice metaphor, @JakeV8 !
@JakeV8, you are right, the thing is I get the problems but not how to write them or solve them sometimes.
I have the answer to this problem: h=17.09 but the problem says full hours, so would the answer be jus h=18 hours?
You are lucky then.... some people have a hard time seeing it. Just need to develop the discipline to set it up correctly (don't ignore stuff that matters, but do ignore stuff that doesn't), pick the appropriate plan or math technique, then check your answers and think about whether it makes any sense at all.
I still agree with all that JakeV8 says.
So the four step method seems to set up a framework that will hopefully guide people to understanding the whole picture.
Part 4: Check and interpret. 17.09 is the math answer, but when you interpret, you realize that your boss will not allow you to leave after 0.09 hours...less than 6 minutes into your 18th hour of work... and even though 17.09 is the closest full hour, 17 hours at 5.85 per hour isn't enough to make $100. Need to round up to 18 full hours, even though you will make slightly more than $100.
ok. next 5. Suppose you have $15.00 to plant a vegetable garden. If you spend $6.00 on seeds, how many packs of vegetable plants could you buy for $0.75 each?
Your teacher might be going for that, or maybe not! But I'd include both 18 hours and 17.09 hours if that was the answer.
yes, I agree with @theEric as long as you can provide both answers AND your reasoning. A lot of these classes seem to make you submit a single answer with no reasoning... then you just have to pick the best approach you can. There is no objectively correct answer between 17.09 and 18... it just depends on the assumptions the problem-author made when setting it up.
On #5, what info do you need to find? What will your plan be?
so first i know that I have $15.00, I can spend $6.00 on seeds and I want to know how many packs of veggie plants I can buy at $0.75 each. So far I have: let p= veggie plants
1. I admire your willingess to learn and work this out. 2. Now I'll get back to the problem.
@jgurl.3958 can you "devise a plan" and come up with the equation for how many plants, p, you can buy if you start with $15, and then spend $6 on seeds? You also know each plant costs $0.75
hint: whenever you have an "each" situation, it is often looking at multiply the "number of things" times the "amount each" like "cups of lemonade" times "50 cents each"
Sorry if I'm slow. Either OpenStudy or connection is being slow and making it difficult to type. I might restart my computer..
yes, that works :) Good job. You could have also said 15-6 = 0.75p which would be the same result as yours Your plan is "$6 plus "p" plants at 0.75 each" must equal $15 My plan was the almost the same, but I said "start with 15, spend 6 on seeds to leave 9, and then divide 9 by the price per plant, 0.75. Bottom line, your plan is great... please continue :)
got it. last question: 6. The SGA makes a profit of $126.00 selling bags of popcorn. If their expenses were $22.50, how many $1.50 bags of popcorn did he sell? Use mathematics to justify your answer.
this one is almost identical to the lemonade question...
so 126=1.5p-22.5 ?
nicely done... now solve for p
@jgurl.3958 all good?