Tutor profile: Chris B.
You're making cookies with your grandmother for your whole family as a dessert after dinner. There are going to be 12 people at dinner, and you have 5 cookies in the oven baking currently. How many more cookies do you need to make so that everyone at dinner can have a cookie for dessert?
This problem may seem a bit tricky, but when we break down this word problem, we see it's not so hard! Let's look closer at the wording of the problem and see what clues we can find. Our first clue is that the question asks us "How many more...". When a question asks us "more", it usually means we're going to have to add to our total to find the number we're looking for! Let's also get some of the wordiness out of the way. Don't think too much about the scenario; focus on the numbers and what we're being asked. We know we want 12 cookies, and we only have 5 right now. Now we can solve our problem! Remember, we're going to need to add cookies to the 5 we already have in order to get 12. So, let's rephrase that a bit: 5 plus what equals 12? So, let's think: what number can we add to 5 to get 12? That's right! 7! So, we need 7 more cookies in order for everyone at dinner to get a cookie for dessert! Great job!
How do you play a C chord on the guitar?
The guitar is a really interesting instrument because there are actually multiple ways to play every chord there is! For the sake of simplicity, let's start with the standard way guitar players play a C chord. First, pick up your guitar and place your left thumb behind the neck of the guitar, the long, straight piece of wood between the head (where the tuning knobs, the silver pegs, are), and the body (the fat part of the guitar). After we're comfortable holding it, let's start with our left ring finger. This is going to play the root note of our chord, C. Take your left ring finger and place it on the 3rd fret (marked by the first white dot on the neck as you're looking down at it) of the 5th string, the one below the thickest, low string. Press down firmly and pluck the 5th string a couple of times with your right thumb to make sure the note is ringing out correctly. If it sounds a bit buzzy, try pressing harder! Next, let's take our left middle finger and put it on the 2nd fret (one fret to the left of the third fret where your ring finger is) of the 4th string, one string below the 5th string as you're looking down on the neck. Make sure to press down firmly! Now, use the thumb of your right hand to pluck the 5th string and 4th string one after another to make sure both notes are ringing out correctly. If the notes sound buzzy, again, try and press down a bit harder. Also, make sure no parts of your hand or fingers are touching the strings! Now it's time to put our last finger down! While keeping our other two fingers on our strings, let's take our left pointer finger and place it on the 1st fret (one fret to the left of the 2nd fret where your middle finger is) of the 2nd string, which is the one above the highest, thinnest string. Again, press down firmly! Like before, let's take our right thumb and pluck the 5th, 4th, 3rd, and second string one after another (the 3rd string should have no fingers on it) and let all the notes ring out. If you hear that buzzy sound, again, make sure you're pressing down as hard as you can and that no parts of your fingers or hand are touching any of the other strings! Lastly, let's learn how to strum a C chord. This is really easy - all we want to do is drag our right thumb across all of the strings except for the 6th string, the thickest string that's closest to you when looking down on the neck. And there you have it; you played a C chord!
Say you have $200 to spend. You go to the electronics store and see that video games cost $20 and movies cost $15. You leave the store with 11 items combined and $5 left over. How many of each item did you buy?
In order to solve this problem, we must use a system of equations. Let's start by setting the number of video games we bought equal to the variable x, and the number of movies we bought equal to the variable y. Since we know that we have 11 total items, we can write the following equation: x + y = 11. This is a good start, but we still have two unknowns! We need another equation. Let's start this one by figuring out how much money we spent in total. Subtracting the amount of money we started with from the amount of money we walk out of the store with, we see that $200 - $5 = $195 So we spent $195 at the store. Additionally, we know from the information in the problem that video games cost $20 and movies cost $15. Remembering that the variable x = the number of video games we bought and y = the number of movies we bought, we can write down a very similar equation to our first equation and say that 20x + 15y = 195 We can make this statement because multiplying x, the number of videogames we bought, by 20, the cost of one video game, will give us the total amount that we spent on all of the video games, and multiplying y, the number of movies we bought, by 15, the cost of the movie, will give us the total amount we spent on all of the movies. Adding these two numbers will give us 195, the total amount we spent at the store. Now it's time to solve our system of equations. I find it easiest to start with the first equation, x + y = 11. By subtracting y from both sides, we can isolate the variable x and obtain the following equation: x = 11 - y Now that we have isolated the variable x, we can plug in this value of x to our second equation, 20x + 15y = 195. Doing so gives us the following equation: 20(11-y) + 15 y = 195. Now we have an equation with only 1 unknown! This means we can solve for y. The first step is to distribute the 20 into each number in the parentheses, which means we must multiply. This gives us the equation 220 - 20y + 15 y = 195. Now we want to isolate y on one side of the equation, so we must combine the two y terms and subtract the 220 over to the other side. -20y + 15y = -5y, and 195 - 220 = 25. So, we can rewrite our equation as -5y = -25 Now, all we have to do is divide the -5 away from the y, and we have our answer! So, y = -25/-5 a negative number divided by a negative number is a positive number, so y = 25/5 25/5 = 5, so we can say that y = 5! We're halfway there! Now that we have our value of y, we can obtain our value of x by plugging in our value of y into one of our first two equations. Let's pick the first one, as it is a simpler equation overall. Again, that first equation we wrote down is x + y = 11 So, because we know that y = 5, we plug 5 into that equation wherever we see y. This gives us the equation x + 5 = 11. Now all we have to do to find our value for x is subtract 5 from both sides of the equation! 11 - 5 = 6, so we can write x = 6 We got it! So, we bought 6 video games and 5 movies, and have $5 left to spare! Good job!
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