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Read the attached files. First read the one entitled "Read

this first" and then open the file called "Systems of Equations Problems with Answers"


Pick ONE of the problems that has not already been solved, and demonstrate its solution for the rest of us.

Select Post New Thread and make the problem number and topic (#10 Jarod and the Bunnies) the subject of your post.

The answers are at the end of the file so don't just give an answer - we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!

This is a moderated forum. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order to get credit.

Questions 1,2,3 has already been done

Forum: If Only I Had a System… Applications of Systems of Linear Equalities The Problem: When students are surveyed about what makes a good math Forum, at least half of the responses involve " discussing how to work problems " "seeing how this math applies to real-life situations " This Forum on applications of systems of equations addresses both of these concerns. Unfortunately , the typical postings are far from ideal . This is an attempt to rectify the situation. Please read this in its entirety before you post your answer! Pick-up games in the park vs. the NBA: Shooting hoops in the park may be lots of fun, but it scarcely qualifies as the precision play of a well-coached team. On the one hand, you have individuals with different approaches and different skill levels, "doing their own thing" within the general rules of the game. On the other hand you have trained individuals, using proven strategies and basing their moves on fundamentals that have been practiced until they are second nature. The purpose of learning algebra is to change a natural, undisciplined approach to individual problem solving into an organized, well-rehearsed system that will work on many different problems. Just like early morning practice, this might not always be pleasant; just like Michael Jordan, if you put in the time learning how to do it correctly, you will score big-time in the end.
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But my brain just doesn't work that way. . . Nonsense! This has nothing to do with how your brain works. This is a matter of learning to read carefully, to extract data from the given situation and to apply a mathematical system to the data in order to obtain a desired answer. Anyone can learn to do this. It is just a matter of following the system; much like making cookies is a matter of following a recipe. "Pick-up Game" Math It is appalling how many responses involve plugging in numbers until it works. "My birthday is the eleventh, so I always start with 11 and work from there." "The story involved both cats and dogs so I took one of the numbers, divided by 2 and then I experimented." "First I fire up Excel. .." "I know in real-life that hot dogs cost more than Coke, so I crossed my fingers and started with $0.50 for the Coke. .." The reason these "problem-solving" boards are moderated is so that these creative souls don’t get everyone else confused! NBA Math In more involved problems, where the answer might come out to be something irrational, like the square root of three, you are not likely to just randomly guess the correct answer to plug it in. To find that kind of answer by an iterative process (plugging and adjusting; plugging and adjusting; . ..) would take lots of tedious work or a computer. Algebra gives you a relative painless way of achieving your objective without wearing your pencil to the nub. The reason that all of the homework has involved x's and y's and two equations, is that we are going to solve these problems that way. Each of these problems is a story about two things, so every one of these is going to have an x and a y. In some problems, it’s helpful to use different letters, to help keep straight what the variables stand for. For example, let L = the length of the rectangle and W = the width.
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Systems of Equations 1) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot dogs and 4 bags of potato chips for $9.25. Find the cost of each item. 1) 2) University Theater sold 556 tickets for a play. Tickets cost $22 per adult and $12 per senior citizen. If total receipts were $8492, how many senior citizen tickets were sold? 2) 3) A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $36.12. The second group bought 6 slices of pizza and 6 soft drinks for $31.74. How much does one slice of pizza cost? 3) 4) Tina Thompson scored 34 points in a recent basketball game without making any 3 - point shots. She scored 23 times, making several free throws worth 1 point each and several field goals worth two points each. How many free throws did she make? How many 2 - point field goals did she make? 4) 5) Julio has found that his new car gets 36 miles per gallon on the highway and 31 miles per gallon in the city. He recently drove 397 miles on 12 gallons of gasoline. How many miles did he drive on the highway? How many miles did he drive in the city? 5) 6) A textile company has specific dyeing and drying times for its different cloths. A roll of Cloth A requires 65 minutes of dyeing time and 50 minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing time and 30 minutes of drying time. The production division allocates 2440 minutes of dyeing time and 1680 minutes of drying time for the week. How many rolls of each cloth can be dyed and dried? 6) 7) A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the bills is $780. How many $5 bills are there? 7) 8) Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 2 times as many dimes as nickels, and the value of the dimes is $1.65 more than the value of the nickels. How many nickels and dimes does Jamil have? 8) 9) A flat rectangular piece of aluminum has a perimeter of 60 inches. The length is 14 inches longer than the width. Find the width. 9) 1
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10) Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 8 feet more than 3 times the width. He needs 64 feet of fencing to do the job. Find the length and width of the garden. 10) 11) Two angles are supplementary if the sum of their measures is 180°. The measure of the first angle is 18° less than two times the second angle. Find the measure of each angle. 11) 12) The three angles in a triangle always add up to 180°. If one angle in a triangle is 72° and the second is 2 times the third, what are the three angles? 12) 13) An isosceles triangle is one in which two of the sides are congruent. The perimeter of an isosceles triangle is 21 mm. If the length of the congruent sides is 3 times the length of the third side, find the dimensions of the triangle. 13) 14) A chemist needs 130 milliliters of a 57% solution but has only 33% and 85% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. 14) 15) Two lines that are not parallel are shown. Suppose that the measure of angle 1 is (3x + 2y)°, the measure of angle 2 is 9y°, and the measure of angle 3 is (x + y)°. Find x and y. A) x = 324 7 , y = 36 7 B) x = 36 7 , y = 324 7 C) x = 36 7 , y = 288 7 D) x = 288 7 , y = 36 7 15) 16) The manager of a bulk foods establishment sells a trail mix for $8 per pound and premium cashews for $15 per pound. The manager wishes to make a 35 - pound trail mix - cashew mixture that will sell for $14 per pound. How many pounds of each should be used? 16) 2
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4) Tina Thompson scored 34 points in a recent basketball game without making any 3-point  shots. She scored 23 times, making several free throws worth 1 point each and several field goals worth two points each. How many free throws did she make? How many 2-point field goals did  she make?  --------------------------------------------------------------------------------------------------------------------- ------------------------------------------- Solution Process: Let "x" = the number of 2-point field goals scored Let "y" = the number of free throws scored Equation 1:  x + y = 23 23 is the total amount of shots taken. I know Tina only made 2-point field goals and free throws,  so we can create a basic equation depicting just that. Equation 2:  2x + y = 34  34 is the total amount of points Tina scored. Since x is equal to a 2-point field goal, we need to  multiply x by 2, and leave y alone since it is only a 1-point shot. --------------------------------------------------------------------------------------------------------------------- ------------------------------------------- Method to Solve: Let's continue by using the Substitution Method for solving this: Equation 1:  x + y = 23 (Solve for y) y = -x +23  Plug this into equation 2 in order to solve for y Equation 2:  2x + y = 34 (Substitue y)
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2x + (-x + 23) = 34 (Solve for x) x + 23 = 34 (Subtract 23) x= 11 ; We know x is equal to the 2-point field goals, so now we need to plug x (11) into  Equation 1 to find out how many free throws were made. Equation 1:  x + y = 23 (Plug in x, and then solve for y) 11 + y = 23 (Subtract 11) y = 12 ; We know y is equal to the free throws. Now we can answer the initial  question. --------------------------------------------------------------------------------------------------------------------- ------------------------------------------- v Answer: Tina made 12 free throws and 11 2-point field goals. A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $36.12. The second group bought 6 slices of pizza and 6 soft drinks for $31.74. How much does one slice of pizza cost? To solve this problem, I would like to put X for the price of pizza and Y for the price of soft drinks. The first group paid $36.12 for 8 slices of pizza and 4 soft drinks. Thus, 8x + 4y= 36.12 (1) The second group paid $31.74 for 6 slices of pizza and 6 soft drinks. Thus, 6x + 6y = 31.74 (2) I am going to use addition method to solve this problem because no variable has coefficient of 1 or -1. 1. Mutiply equation (1) by -3 -3(8x) + (-3)(4y) = (-3)(36.12) -24x - 12y = -108.36 (3)
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Subject: College Algebra, Math

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