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Video transcript

we're told that Mika can eat 21 hotdogs in 66 minutes she wants to know how many minutes em would it take her to eat 35 hotdogs if she can keep up the same pace so a big clue is the same pace it'd have to remove a hair from my tongue all right a big a big clue is the same pace that means that the hot dogs hot dogs per minute per minute is going to be constant is always going to be the same always the same always the same because this is essentially the pace our hot dogs per minute are going to stay the same is going to stay at the same pace so we it tells us that you can eat 21 hot dogs in 66 minutes so our hot dogs per minute at least up here it's 21 hot dogs in 66 minutes so 21 hot dogs in 66 minutes well if her pace is always going to be the same well it's going to take her this ratio over here is going to be the ratio between 35 hot dogs and however long it takes her to eat 35 hot dogs so once again hot dogs per minute are go it has to be a constant because it's going to be the same pace hot dogs per minute if it takes 21 hot dogs takes 66 minutes 35 hot dogs take em minutes these two ratios are going to be the same we're dealing with a proportional relationship that's going to be happening at the same rate and then we're left with a situation where we just have to solve for M and there's a bunch of different ways that you could tackle this the easiest way that I can think of doing it is I like I don't like this M sitting here in the denominator so let's multiply both sides by M let me do that in a different color so I multiply that side by M and then this side by M and so what do we get on the left-hand side we have 21 over 66 M 21 or 66 times M times M is equal to is equal to well you divide by M and multiply I am those are going to cancel out you're just going to have 35 and now you just have to solve for M and the best way I can think of doing that is multiply both sides times the reciprocal on both sides times the reciprocal of the coefficient on the M so let's multiply both sides by let's multiply both sides by 66 over 21 once again I've just swapped the numerator and the denominator here to get the reciprocal but I can't just do it to one side of an equation I have to do it to both sides otherwise it's not going to be an equate it's not going to be equal anymore so times 66 over 21 this is just going to be one you multiply something times its reciprocal you're just going to end up with one so you're going to be left with M is equal to now 35 times 66 divided by 21 well 35 is the same thing as 35 is 5 times 7 and 21 is 3 times 7 so you're multiplying by 7 up here and here you have a 7 in the denominator you're dividing by 7 so they are going to cancel out so this is going to simplify to 5 times 66 over 3 and then we could simplify it even more because 66 is the same thing as 3 times 22 3 times 22 and so you have a 3 in the numerator you're multiplying by 3 and a 3 in the denominator dividing by 3 3 divided by 3 is 1 so you're left with 5 times 22 which is 110 so it would take her M minutes to eat 35 hot dogs at the same pace now when some of you might have tackled it you might have had a different equation set up here instead of thinking of hotdogs per minute you might have thought about minutes per hotdog and so in that situation if you thought in terms of minutes per hotdog you might have said okay look it took Micah 66 minutes to eat 20 to eat 21 hot dogs and it's going to take her M minutes to eat 35 hot dogs and if it's the same base then these two rates are going to be equal they have to be the same pace and so then you can solve for M and actually this one's easier to solve for him you just multiply both sides by 35 multiply both sides by 35 and you're left with on the right-hand side you're left with just an M and on the left-hand side same same idea you're taking 35 you have 35 times 66 twenty-firsts which we already figured out is 110 so 110 is equal is equal to M so once again multiple ways to tackle it but it's important that we got the same answer