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# Writing a System of Equations

by Maria
(Columbia)

Find the equations to: Alice spent \$131 on shoes. Sneakers cost \$15 and Fits cost \$28. If she bought a total of 7 shoes, then how many of each kind of shoe did she buy?

### Karin from Algebra Class Says:

Hi Maria,

With this direction, you are being asked to write a system of equations. You want to write two equations that pertain to this problem.

Notice that you are given two different pieces of information. You are given information about the price of the shoes and the number of shoes bought.
Therefore, we will write one equation for both pieces of information.

First we will define our variables. The information that we don't know is how many of each kind of shoe was purchased.

Let x = Sneakers
Let y = Fits

Our first equation based on price is:
15x + 28y = 131

The second equation based on number is:
x + y = 7

You now have two linear equations based on this one problem. You can solve the system of equations to find out how many of each type of shoe you have.

Hope this helps,
Karin

### Comments for Writing a System of Equations

Average Rating     Jun 22, 2016 Rating   HELP!!! by: Anonymous Solve by writing system of equations. Mr.Chandra bought 2 lbs. of cheddar cheese and 3 lbs. of chicken loaf. He paid \$26.35. Mrs.Hsing paid \$18.35 for 1.5 lbs. of cheese, and 2 lbs. of chicken loaf. What was the price per pound of each item?

 Feb 01, 2016 Rating     Subsitition equ by: Anonymous I don't get this-- Isaac bought a total of 32 pieces of candy. He bought 3 times as many chocolate as he did hard candies. Write and solve by substitution a system of equations to represent this sceniro--- how do you write one

 Oct 19, 2015 Rating     HELP by: Anonymous How do I write this problem as an equation so I can solve it?An artist is going to sell two sizes of prints at an art fair. The artist will charge \$20 for a small print and \$45 for a large print. The artist would like to sell twice as many small prints as large prints. The booth the artist is renting for the day costs \$510. How many of each size print must the artist sell to break even?__________________________________________________Solution from Algebra-class.comWe need to write two equations. 1. The cost 2. The number of small prints based on large prints.Let x = number of small printsLet y = number of large prints1. Our first equation is about the pricing:20x + 45 y = 510. (It's \$20 for a small print and \$45 for a large print. Since he wants to break even, this must equal the cost of renting the space which is \$510.2. The second equation is about the number of prints. The problem says: "The artist would like to sell twice as many small prints as large prints".So, x = 2yNow that you have two equations, you can solve the system of equations. The best way to solve this system is to use substitution. Hope this helps!

 Jan 21, 2015 Rating     System of equations by: Anonymous In a class, 45 students take the SAT exam. The number of boys is 8 more than the number of girls.

 Dec 16, 2014 Rating     Writing equations by: Anonymous How do you write an equation for this? Alexis and Kate are both traveling to Europe but Kate is going to France and Alexis is going to Spain. Round trip for Spain is \$820 and a round trip to France are \$1,205. Then Alexis found a nice hotel for 110.50 per night and Kate found a small room for \$75.50 per night. The girls spent the same amount of money on their flights and their rooms and they were on vacation for the same number of days.

 Sep 28, 2014 Rating     Please helppp by: Pistol Tom has 5 comic books and will receive 5 new comic books each month. Jose has 145 comic books and is selling 15 comic books a month. In how many months will they have the same amount of comic books and how many comic books will that be? The variable _____ represents the _______________. The variable _____ represents the _______________. Equation 1: ______________________________ Equation 2: ______________________________

 Nov 19, 2013 Rating     please help by: Anonymous sarah and keith purchased 40 stamps, a mixture off 44 cent and 20 cent stamps. Find the number of each type of stamp if they spent \$16.40

 Sep 13, 2013 Rating     Please Solve by: Anonymous The winning entry at a cake baking contest was an Italian Cream Cake.The perimeter of the rectangular cake was 46 inches. The length was 4 less than twice the width l. Find the length

 Sep 13, 2013 Rating     Please Solve by: Anonymous The winning entry at a cake baking contest was an Italian Cream Cake.The perimeter of the rectangular cake was 46 inches. The length was 4 less than twice the width l. Find the length

 Mar 04, 2013 Rating     help by: Anonymous Jorge paddles his canoe 4 miles in 1 hour . The return trip upstream takes 2 hours. What is Joe's rate?

 Feb 27, 2013 Rating     Writing systems of equations that represents the charges by: Anonymous Jenny charges \$4 per day to pet sit. Tyler charges \$2 up front, and then \$3 per day to pet sit.Write a system of equations that represents the charges.____________________________________________________Your answer by Karin from Algebra-class.com:You want to write two equations. One equation will represent Jenny's wages and the other will represent Tyler's wages. First identify your variable. You don't know how many days each pet sits, therefore:Let x = the number of days pet sittingJenny: 4x (means \$4 per day)Tyler: 2+3x (means \$2 up front +\$3 per day)Hope this helps.Karin

 Jan 23, 2013 Rating     Please Help by: Anonymous Sophie remebered looking in her purse counting all the coins she had and it added up to be thirty coins , all DIMES and NICKELS. She also remember that yhe value was worth \$2.60 . How many nickels are there in Sophies Purse?

 Jan 15, 2013 Rating     Systems by: Anonymous Liz and Ashley buy a radio for \$128. Liz paid \$36 more than Ashley. Write a system to help determine the amount each paid. Confused

Nov 09, 2012
Rating     how do i write this

A group of 36 people attend a ball game. There were twice as many children as adults in the group.

How do I write this as a system of equations without solving?

### Karin from Algebra Class Says:

Let a = adults
Let c = children

a + c = 36
c = 2a

Hope this helps!
Karin

 Sep 19, 2012 Rating     Writing a System of Equations by: Anonymous Please help with this problem:During one calendar year, a state trooper issued a total of 375 citations for warnings and speeding tickets. Of these, there were 37 more warnings than speeding tickets. How many warnings and how many speeding tickets were issued?____________________________________________________Karin Says:We must first identify our variables. Our two unknowns are: the number of warning and the number of speeding tickets.So...Let x= the number of warningsLet y = the number of ticketsWe know that 375 warning and tickets were issued in all. That equation is: x+y = 375We also know that 47 more warning were given out than speeding tickets, so that means: x = y+ 37Our system of equations is:x+y = 375x = y+37Now to solve:I would use the substitution method since one of the equations is solved for x.We'll substitute y+ 37 for x into the first equation.x+y = 375 - substitute y+37 for xy+37 +y = 3752y +37 = 375 Combine like terms2y + 37-37 = 375 - 37 Subtract 372y = 3382y/2 = 338/2 Divide by 2y = 169Since we let y = the number of speeding tickets, we know that 169 speeding tickets were issued.We also know that x = y+37 x = 169+37 x = 206So, 206 warnings were issued.Final Answer:169 speeding tickets206 warningsI hope this helps you to solve the problem.Karin

May 23, 2012
Rating     Please tell me how i would start to solve this, Your teacher is giving you a test worth 100 points. There will be 40 questions on the test some worth 2 points and others 4 points. How many of each question are on the test?

### Karin From Algebra Class Says:

This is one of the most common types of system of equations problems.

Remember that when you write a system of equations, you must have two different equations. In this case, you have information about the number of questions AND the point value for each of the questions.

Therefore, one equation will be written about the number of questions. The other equation will be written about the point values.

We know that there are two types of questions on the test, so let's define our variables:

Let x = the number of 2 point questions
Let y = the number of 4 point questions

Equation 1: Number of questions.
(The problem says that there are 40 questions total)

x+y = 40

Equation 2: Point value of questions.
(We know that some questions are worth 2 points and others worth 4 points. There is a total of 100 points for the test)
2x + 4y = 100

This leads us to our system of equations:
x+y = 40
2x+4y = 100

Hope this helps!

Karin

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