6th grade (Eureka Math/EngageNY)
Sal uses rates to solve word problems. For example, Lynette can wash 95 cars in 5 days. How many cars can Lynette wash in 11 days?
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- Fact" Author writes 5 pages in 3 hours
3 hours= 3x60= 180 minutes .
he writes 5 pages in 180 minutes ...
Divide 180 by 5, so he takes 36 minutes to write one page.
Thew Question: how many pages can he write in 8 hours?
8x 60 is 480 minutes.
Then divides minutes per page into available (5 hours) minutes, so..
480 divided by 36 is 13.3333 etc. But evidently that's not correct.
Where did I go wrong?(3 votes)
- Great documentation of the method and reasoning you used!
You are correct in your calculations and conclusions, so probably just needed the answer in a different form.
Since 13.333333… must be written as a rounded decimal, or truncated, it becomes an approximation.
It's likely the answer needed to be entered as an exact equal value, rather than a rounded 'close to correct' decimal.
★ Here's an easy way to arrive at the answer…
Set the ratios in proportion to each other.
Put both ratios in the same order.
You can arrange them either way, as long as both ratios match.
Let's go with…
Pages to Hours
An author writes at a rate of:
5 pages to 3 hours = 5 to 3
How many pages in 8 hours?
p = pages
? pages to 8 hours = p to 8
★ p to 8 and 5 to 3
p/8 = 5/3 ←ratios in proportion
3p = 8 • 5
3p = 40
p = 40/3 pages in 8 hours ←🥳
p = 13 1/3 pages in 8 hours
p ≈ 13.333333…
The author writes thirteen and one third pages per eight hours.
•Fraction form 40/3 is an exact answer (some say improper fraction because numerator is larger than denominator)
• Mixed Number form: 13 1/3, sometimes used as an answer, if directly asked for in the directions, mathematically it means 13+1/3.
•If they want how many full pages, the author completes 13 whole pages per 8 hours.
(≧▽≦) I hope this helps.(8 votes)
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- I don't get it why do we have to divide 95 days by 11 and 5 day by 11(3 votes)
- you need to divide 95 by 5 not eleven because 95 divided by 5 is 19 which is the number of cars linete washes in one day and then you multiply that by 11 to get how much cars he washes in 11 days.(1 vote)
- [Instructor] So we're told that Lynnette can wash 95 cars in five days. How many cars can Lynnette wash in 11 days? So like always, pause this video and see if you can figure this out. So the way that I would like to tackle it is given the information they gave us, 95 cars in five days, can we figure out how many cars she can wash per day? How many cars in one day? And then we could just multiply that by 11 to figure out how many she could wash in 11 days. So there's 95 cars in five days and so instead of five, if we were to say one day, one day, well, to go from five days to one day, we divide by five. So the number of cars she can do in one day, that would be that divided by five. In either case, we would divide by five and what's 95 divided by five? You might recognize that well, look, five times 20 is equal to 100. So five times 19 is 95. So you might recognize that's 19 cars in one day or if that math I just did seems a little bit too fast, you could just take five into 95. Five goes into nine one time, one times five is five, subtract, nine minus five is four, bring down that five, five goes into 45 nine times, nine times five is 45 and it goes in perfectly. There's no remainder. So all I did is I divided both of these numbers by five to figure out how many she can wash per day. So she can wash 19 cars in one day, 19 cars per day and so if I wanna figure out how many she can wash in 11 days, so in 11 days, well, now, I am just multiplying by 11. So if I multiply 19 times 11, what am I going to get? Well, if you're good at the mental mathematics, you might recognize 19 times 10 would be 190 and then you would have one more 19 so that would be 209 cars or you could just multiply 19 times 11. One times 19 is 19 and then one times 19 is 19. Add 'em together, you get 209. So she can wash 209 cars in 11 days. Let's do another example. Here, we are told at the market, eight batteries cost $10. How much do six batteries cost? Once again, pause this video and try to figure it out. Well, I'm gonna do the same technique. If eight batteries cost $10, let's figure out how much one battery costs. So one battery costs what? Figure that out. Well, it's going to be 1/8th. To go from eight to one, I divide by eight. So what happens when I divide 10 by eight? That's gonna be my per battery cost. So 10 divided by eight is the same thing as 5/4 which is the same thing as one and 1/4 which is the same thing if we're talking in terms of money, it might be more useful to write it like one and 25 hundredths or one battery costs $1.25. And so when they're saying six batteries, how much do six batteries cost, well, if we're going to six batteries cost, we're multiplying the number of batteries times six now. So what's $1.25 times six? So it's gonna be $6 plus another $1.50 'cause six times 25 is 150. So it's gonna be $7.50 and just to make sure the math I just did was right, let's multiply $1.25 times six. Six times five is 30. Six times two is 12 plus three is 15. Six times one is six plus one is seven and we have a total of two digits behind the decimal so there you have it, you have $7.50. Now, there's other ways that you could tackle this. You could say that hey, this is, six batteries is gonna cost 6/8ths as much as eight batteries but that's a little bit confusing, at least for my brain. I like to go just down to the unit cost you could say, the cost per battery and then multiply it by six. It gives me more comfort in understanding what I'm doing.