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43 . Solve the following system of equations graphically: (7 marks) x+J =2 ~y =-5r + 10 44. In order to increase his sales shopkeeper mixes two types of hard candy:...

Question

43 . Solve the following system of equations graphically: (7 marks) x+J =2 ~y =-5r + 10 44. In order to increase his sales shopkeeper mixes two types of hard candy: peppermints and cinnamon candies: The peppermints sell for $1.80/kg. The cinnamon candy sells for $2. A0/kg: The new candy mixture sells for $2.16/kg The shopkeeper makes up 50 kg of the new mixture: Use graph to determine the amount ofeach type of candy that i8 needed to make the new mixture_ Verify your answer: (If you prefer; use

43 . Solve the following system of equations graphically: (7 marks) x+J =2 ~y =-5r + 10 44. In order to increase his sales shopkeeper mixes two types of hard candy: peppermints and cinnamon candies: The peppermints sell for $1.80/kg. The cinnamon candy sells for $2. A0/kg: The new candy mixture sells for $2.16/kg The shopkeeper makes up 50 kg of the new mixture: Use graph to determine the amount ofeach type of candy that i8 needed to make the new mixture_ Verify your answer: (If you prefer; use The Geometer's Sketchpad" or a TI-83 Plus graphing calculator to draw your graph: Include hard copy with your calculations, by printing the graph ) marks) 45 . A local fitness club has two payment options Plan A: monthly membership fee of $25, plus $2 per visit Plan B: fee of $7 per visit Determine the number of visits when both options are the same: Verily your answer; (6 marks)



Answers

Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class $X$ took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. (ii) 5 pencils and 7 pens together cost $? 50$, whereas 7 pencils and 5 pens together cost $? 46 .$ Find the cost of one pencil and that of one pen.

Okay, lets see how we can make a system of three equations given a word problem. And for this one, we're going to say that we have three different kinds of pie. We'll call X, are chocolate cream and will say, Why is our whole and see Miss Cherry. Okay, so how do we create our equation? Well, we know that every day the bakery makes a total of 50 pasts. That means the some of the chocolate, apple and cherry it's gonna total 50. So our first equation is going to be X. That's why plus Z is equal to 50 pies. Okay, now we want to know how much revenue we will make in a day. And what, Rick, what equation with reference sent the revenue. So if we know for example, that we can sell a chocolate pie for $5 you would take $5 on a number of pies and we can sell. Apple applies for $6 so $6.10 is the number of apple pies, and we can sell cherry pies for $7 so seven times the number of terrifies. And when we add all that up, it's going to total 295 each day. And lastly, how does our cost figure in if we have a total cost each day for our pies of 145? How do we represent that? Well, it costs us $2 to make a chocolate pies or two times the number of chocolate pies. And it costs us $3 to make an apple pie. And it costs us $4 to make a cherry pie, and the total of that cost is gonna add up to 150. So there, you see, we have our system of three equations to represent this problem.

Talk a little bit. Let's talk a little bit about what we know from this problem. So we have three different kinds of products. We, uh, chocolate cream, which sells for $5 and it costs $2 or $5 $2 and it wants us to represent Ah, this pie with X. Then we have Apple, which sells for six and cost three. Have a whole sells for six cost three Represented by why and lastly, we have cherry, which shows for seven cost for represented by sea seven. Core busy. So now let's start working on our equations So we know that they so 50 pies so that would be each one of them added together could get us to 50 thin. Our revenue is 295 which that would be what we sell them for. So I'm gonna take each one times what we sell them for. So five x a six y plus seven z then our cost is 100 and $45. So that would be times this other times cost. Call him So we know two x so us three why plus or C? And that was the our three equations

So Hello, Shane. Now we're good left in this question. And let lift X re Prigent in the number off kick sword kick sword. So first the cost price Quito A $40. The cost was the babys hair and two point powder for making each cake. So 2.50 x plus 40 no be revenue generated. So every new because 6.5 Europa take 6.50 a ticket. See, it is giving the optics and seeks both adequate. So 6.50 x equal toe to find 50 X plus 40. No, that's all this. So 6.5 years X minus 2 100 This is poor When Jiro Jiro X people are put so finally X equal to 10. So it is then no more Arctic sold. No, my daughter. Good off. So this is the drop and this is a graph optics equal toe 6.50 x and this is C X gosh which is good 0.5 x plus 40. Now, this is a point of intersection which is given, uh, X this 40 not for 10. This is X, then nice of soup 10 over here a lot. 65. So this point we can say the CDA $65 But when less than deck 10 cake will be sold. So you see the cost place Revenue is below the cost place. So revenue less than cash place. So he will be in the loss. So when X is less than 10 better we lost or when X is better than then, that is a prophet x equal depend no property, daily loss.

For this question. We're told one ounce of coffee sells for a dollar 70. Now we're told that two ounces of coffee So for $3. 20 we're for parts. They were US company in question for this. So to start off with we want a friend are slow, so we know ourselves is equal to 3.2 minus 1.7 over two minus one, which will get us 1.5. So we know that our quick, sudden looking, plugging warmer valleys of 1.7 is equal to 1.5 turns. One plus B, which will get US B, is equal to 0.2. So our question for a line so it costs over coffee is able to 1.5 times our number of ounces, plus their appointed to so For Parts B year asked was the cost of 3.5 ounces of coffee. So we know that our costs is able to 1.5 times 3.5 plus 0.2 and so that will get us the cost. $45.45. So for C were asked, the coffee is marked a six Rs 50 we don't know how many as potentially or six. But we have a cost of $6. 50 is able to 1.5 and plus sterile points to So we say that won't put five earned is able to 6.3. Yes. So that will get us when is equal to 4.2 ounces. So we know that inducts container. There are 4.2 answers of coffee and then for d were asked to graft this so we No Okay, so we have 1.5 backs was there. So we have a graph. So we have one of next plus 2.2 and we know that X is greater than or equal to one. So this is our graph.


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