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Each serving of a certain fruit snack contains 90 calories Han wants to know how many calories he gets from the fruit snacks: Write an equation that shows the numbe...

Question

Each serving of a certain fruit snack contains 90 calories Han wants to know how many calories he gets from the fruit snacks: Write an equation that shows the number of calories, €, in terms of the number of servings,Tyler needs some extra calories each day during his sports season: He wants to know how many 'servings he can have each day ifallthe extra calories come from

Each serving of a certain fruit snack contains 90 calories Han wants to know how many calories he gets from the fruit snacks: Write an equation that shows the number of calories, €, in terms of the number of servings, Tyler needs some extra calories each day during his sports season: He wants to know how many 'servings he can have each day ifallthe extra calories come from



Answers

A one-cup serving of pineapple juice has 9 more than three times as many calories as a one-cup serving of tomato juice. Servings of the two juices contain a total of 173 calories. How many calories are in a serving of each type of juice?

Okay. So for this problem, we are going to be solving a problem based upon calories from fat carbs and protein. So I'm gonna set my ex to be the calories from Fats my white to be my calories from carbs or carbohydrates and then z to be, um my carbs are by calories from proteins. So what I'm going to do is I'm gonna look at the equation. So we were told that Oreos have 10 g of fat, 36 carbs to proteins, and 240 calories. So we're gonna have 10 x plus 36. Why? Plus two z equals 240. Then the next one we have is for Twix. It's 14 14 37 and three for a total of 2. 80. So 14 x plus 37 y plus three z equals 280. And then last, we have our trail mix, which is 2023 11 and 2 95. So 20 x plus 23 y plus 11 z equals 2 95. And so I'm gonna set this up is a matrix. Just use the coefficients. So 10 14 20 36 37 23 23 11 and then to 40 as my answers to 80 and then to 95 and then using a calculator to solve this, we find out that our answers are a total of 8.15 calories, Um, and so you see why will be 4.23 calories and then Z would be 3.15 calories. So the question is asking us, um, how many calories are in each gram of fat carbon protein? So based off our answer, that would be the number of calories for each one of those.

This super part? A. I think a couple of key things with this problem is because there's two pizzas and their 960 calories age we first need to most by that 9 60 by two. Um, so 179 60. We're splitting 1920 calories among n people. And after we split the pizza, each person's gonna have one banana. Okay, so that's that would be our equation for the number of calories and people. He huh? Understood? Kind of sketchy, quick graph of this. Um, we really only need, like, the positive side of the graph. Um, we're going to have a horizontal and center at 100. We're gonna make 100 two. And we are very class until be the y access. Because in you said the denominator equal to zero to find that one. If we were to plug in one like one person eating this, then they would have almost 2000 calories, so that would be like, well, off the page. Um, so playing, too. We'll have that 9 60 plus 100 which is around 10 60. So if if 100 was two dashes, that's +234 5678 on Tess is still off the page of their If we plug in three. Well, it's still divides. Uh, fairly evenly. So three goes into 640 so three would go through 6 40 So there's 100 again, 203 104 by six, and then boarding. There's our first point. If we plug in four will get 400. Um, for 80. Plus who? That last one. Okay, so be 6 40 then plus 107 every 7 40 So let's just go up. Just 7 40 and then 2,000,000,004. We'll get 4 80 plus 100 is five eighties. That's close to 600. 12345 Okay, plug it in five. We'll get three 3 84 plus 100 for 94. 12 345 Okay, well, basically, this crap is just gone. Except for my dad. I'm just approaching the assented of 100. The more people you have, the closer you get to 100 calories per person. Um, part being I just wants to know, like, how many people do we need to make it? 500 calories per person. So 2345 So we already kind of calculated that that's gonna be right at just before five people. Um, so around five people to get 500 calories, I think five people would be less than 500 calories. So if you want to make sure that you get 500 calories, Um, but, like you definitely need four people, we get beyond four people than Ah, you have less than 500 Assumes that beyond for is every less than 500 calories. Okay, Thank you.

We need to eat a number of apples, which I will call X as well as a number of avocados, which I will call. Why So with this in mind, let's figure out how many of each we should eat. We want a total calorie goal of 1000 calories. We know that apple has 100 calories than an avocado has 350. So 100 calories per apple times X apples plus 3 50 calories per avocado times Why avocados equals 1000. We're also aiming to eat 100 grams of carbohydrates. So we know here that one apple has 24 grams of carbohydrates and one avocado has 14 grams of carbohydrates. So 24 x plus 14 y equals 100. Let's get started. So we need to cancel out one of our two variables here. Export Why? And it just so happens that if you multiply 14 by 25 you will get 350. Why does this matter? You'll see in a second. So I'm going to drag this equation over here and now let's consider multiplying the entire bottom equation by negative 25 so that would be on both sides. This will give us negative 24 times 25 or 600 X minus 14 times 25 as we previously said was 350. So minus three and 50 Y is equal to 100 times negative. 25 or negative 2500. All right, so you may have noticed here why I did that. Multiplication. We have 3 50 y and negative 3 50 Why those air going to cancel out if we add the two equations? So let's do just that. We're going to be adding these two that will give us 100 minus 600 or negative 500 X plus zero because those terms will cancel, just as expected, equals 1000 minus 2500 which is just 1500. Sorry, Negative. 1500. Okay, now, if we divide both sides by negative 500 we'll get that X is equal to three. So we will have three apples total, but we're not quite done yet. We also need to figure out how many avocados we need to eat. So let's plug back into our original equation. We have 100 times now three apples instead of acts plus 3 50 times why the number of avocados equals 1000. Well, 100 times three, that is 300 plus 7 50 Why equals 1000? And now we can subtract 300 from both sides. Giving us that should be 3 50 not 7 50 That's just a writing mistake. We should have subtracting three under from both sides. 3 50 y equals 700 and finally dividing by 3 50 will yield that why equals to avocados. So we have determined through algebra that we should be eating three apples and two avocados.

One serving has 102 calories. Stop substituted that for C on DDE. In this equation, we just need to solve for f ah, starting with T subtraction property. I can subtract 90 on both sides on this gives me 12 equals nine f and then I can say bye division property. I divide nine on both sides and these cancel owed. And so I have f equals 12 divided by nine. This can be simplified as four divided by three or just one 1/3. So that's how much that's how many grams of fat are in each serving off serial.


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