Solving Systems of Equation Word Problems Review | Expressions & Equations | Grade 8
Word problems now we’re going to solve the following word problem by using a system, and so by creating a system if there’s things that are unknown in the word problem, we’re going to assign a variable to them. So here we have christian and mark open their savings accounts. On the same day, christian started his account with fifty dollars and plans to deposit ten dollars. Each month mark began his account with thirty dollars and plans to deposit fifteen dollars each month after how many months will christian and mark have the same amount of money in their savings, and what will that amount be? So we start seeing the important information here. We see that there’s, two people christian and mark and christian plans on depositing 50 and each month every month he will deposit 10 each month. So here we have christian now christian his start. He starts with fifty dollars fifty dollars and then deposits or ads 10 par mois. Now this is important for us to get some background information. We need to find out from the word problem and how we can pull that information, so we can set up an equation. Prochain, we have mark now mark he is depositing or he begins his account with thirty dollars and plans to deposit fifteen dollars each month. So here mark he starts with thirty dollars and adds fifteen dollars. He adds more than christian, so he adds fifteen dollars per month. Now our whole goal here is to set it up, set an equation, and so we know that there is a starting amount and then there is each month when i see the word each, i see multiplication when i see per month.
I see multiplication as well, and so i can see that we can set up an equation where we are going to start remember. Our y intercept is always our starting point, so we start with 50 and then we have 10 dollars per multiplication per month, and so the variable x is going to be how many months and the variable y is going to be. How much total will that deposit be so we can start with the second one as well y equals what it is per month, that’s going to be 15 per multiplication times the number of months plus we’re gon na start with thirty dollars already. So this we see this eq. This word problem when we say: okay they’re both in y equals, MX, plus b form or our slope intercept form. So we know that y equals y, and so i can go ahead and say: hey on the left side, Je suis. Going to put 10 x plus 50 is equal to 15 x plus 30., so let’s go ahead and solve for x and once we solve for x, we are going to find the number of months so like off. To the side. Here i could say x is going to equal the number of months that they make a deposit every single month and we’ll find out how many months it’s going to be for christian and mark to have the same amount in their savings. And then why is going to be the amount the total amount in their savings all right? Alors, nous y voilà.
I am going to let’s use this one to add a negative 10x to both sides, which gives that gives me zero. So i will have 50 equals 15 x minus. I mean this looks like a y. Sorry about that guys. It is an x, so 15x minus 10x is 5x plus 30. i’m going to slide this down just a little bit, and so then i am going to add a negative 30 to both sides. So now i have 20 equals 5x i’m going to pull this right over here to the right hand side. So we have 5x equals 20 divide that, by the coefficient of 5 X, is going to equal four, so the number of months so it’s going to be four months that each of the guys will have the same amount of money. Now how much money will they have? That is exactly the same. So by doing that, i can plug in this 4 into either one of the equations and so i’m going to plug it into this first equation. So i’ll have my y value, will give me the amount and then so i’ll have 10. I see the x i’m going to open up with some parentheses plus 50. so i’m going to plug in my 4. Donc, i have y equals 10 fois. 4 est 40 plus, 50 est 90., so mark and christian are gon na have ninety dollars in their savings ninety dollars in their savings in four months.
They will both have the same amount of money in their savings after four months. All right so let’s go ahead and try another one. This was pretty interesting and it just you have to take. Take it one step at a time and really learn to read your word problems and try to pull out the most important information. So let’s go ahead and drag that all the way back here is a new, a new problem. It takes elisha 10 minutes to sketch a black and white drawing and 25 minutes for a color pencil drawing over the weekend. He made a total of nine drawings in two hours, write and solve a system of equations to find out how many drawings of each type elijah made. So here we go with our sketch. Tout d'abord, elijah in 10 minutes took him 10 minutes to have a black and white drawing, and it took him 25 minutes for a color pencil drawing okay. So we have some information there and then we also know that he made a total of nine drawings and it did take him two hours, two hours to do all of those drawings. So when i have all these unknowns or i i need to organize my work just a little bit so here – i’m going to say the variable b i’m going to assign it a variable to it, variable b is going to be the black and white sketch or The black and white drawings to represent the black and white drawings and let’s, see the color pencil i’m going to do c equals the color pencil sketch color pencil drawing.
So i have both of these here. So one thing i see, i see that there’s time i see there’s amount of drawings, so i could easily say let’s see if you agree with me on this – that the black and white drawings plus the color drawings, are going to equal a total of nine drawings. That makes sense, because over the weekend, elijah made a total of nine drawings makes sense. À présent. My second equation for this system is that i’m going to talk about the value or the number amount of time that it took for each drawing. So it took 10 minutes for the black and white drawings plus the 25 minutes for the color drawings equals two hours now i’m going to stop right here, because we have two hours and normally students would say. Oh we’re just going to put a 2 ici, but our minutes and hours. We need to have the same amount of time frame. Whether are we talking about hours or are we talking about minutes so i’m going to convert these two hours to minutes, and i could see that one hour is 60 minutes, so two hours would equal 120 minutes. So so everything – because this is 10 – ce 10 doesn’t represent hours. It represents minutes so over on to the right side of the equation, two hours is equal to 120 minutes. d'accord, i hope you understand that and if not, you can go ahead and re rewind.
This video to help you understand a little bit more about what we’re doing so. It looks right here that we’re going to be doing the elimination method and so i’m going to have to multiply this top by a negative 10.. So what i would get a negative 10, let me rewrite here: we go a negative 10 b minus 10c when i do the distributive property and then a negative 10 fois 9 is equal to a negative 90.. Now i write my second equation: 10 b – and this is a positive 10 b plus 25c is equal to a positive 120.. Excuse me so right away. I see that this negative 10 and positive 10 i’m able to get rid of one of my variables. So i can now just solve for the color pencil drawings, so i have 25c. Minus 10c gives me 15c and 120. Minus 90 gives me 30., so i divide by 15 on both sides and c is equal to two. So it tells me that elijah’s does two color pencil drawings in that weekend. So then i go ahead and i need to plug it in to find out how many black and white drawings he had. So we have our first equation of b. Plus c is equal to nine let’s go ahead and make that a little bit cleaner and so, wherever i see c i’m going to add or input plug in the number two to represent two color pencil drawings.
And so i will subtract 2 on both sides to solve for b. This gives me zero, donc je suis, going to bring the b down and 9 Moins 2 is seven. So it shows me that in this equation, elijah drew two blackened excuse me: two color pencil drawings and seven black and white drawings. So i kind of i want to check my work in checking my work i’m, going to make sure that these numbers are pretty accurate. So the color pencils so i’m going to say c. We had that took 25 minutes times two color pencil drawings. That is a total of 50 minutes that it took elijah to draw both of those color pencil drawings and then my second one, my black and white drawings. Those took 10 minutes each and he drew seven of them so 7 fois. 10 est 70 minutes et 50 et 70 est 120 minutes which equals that two hours that we said up here. So we verified how we solved this problem. We verified that it was two color pencil drawings, so we could say here at the end, elijah drew two color pencil drawings and seven black and white drawings in two hours in two hours period. All right so, ladies and gentlemen, thank you guys so much feel free to watch this video again to help you understand and if you want to hit pause, so you can write all of the steps down in your review is super important, so don’t forget to subscribe.
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