LINEAR EQUATION SYSTEMS WORD PROBLEMS HOW TO

Step 2: Write a system of linear equations Step 3: Solve the system for each variable using the most convenient method Step 4: Check for reasonablenessģ Example 1 At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ How many cones were sold?Ĥ At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ How many cones were sold? STEP 1: Define your variables: Let c = the number of cones sold Let s = the number of sundaes sold STEP 2: Write your system of equations 1.10c s = c + s = 172ĥ At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ How many cones were sold? STEP 3: Solve the equation using the most convenient method 1.10c s = (multiply by 100) 110c + 235s = ( c + s = 172) -110c – 110s = _ 125s = s = 84Ħ At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ How many cones were sold? c + s = 172 c + 84 = _ c = 88 Eighty eight cones were sold.ħ EXAMPLE 2 Your teacher is giving you a test worth 100 points containing 40 questions.

LINEAR EQUATION SYSTEMS WORD PROBLEMS HOW TO

Please note, I know how and have already solved these, so please no answers explaining how to solve them.1 Systems of Linear Equations Word Problems If the owners have hired enough servers to handle 17 tables of customers, how many of each kind of table should they purchase?

Fire codes limit the restaurant's maximum occupancy to 56 customers.

Determine the number of nickels and the number of dimes in the purse.Ī new restaurant is to contain two-seat tables and four-seat tables. What are the two test scores?Ī coin purse contains a mixture of 15 coins in nickels and dimes. The difference between the scores is 12 and the mean, or average, of the scores is 80. How many gallons of each kind of wine must be used?Ī student has two test scores. If the total interest earned for the year was 520 dollars, how much was invested at each rate?Ī wine company needs to blend a California wine with a 5% alcohol content and a French wine with a 9% alcohol content to obtain 200 gallons of wine with a 7% alcohol content.

You invested 7000 dollars in two accounts paying 6% and 8% annual interest. Find the crew's rowing rate in still water and the rate of the current. The return trip upstream, against the current, covered the same distance, but took 4 hours. I thought it might be helpful to provide some examples, verbatim, from the textbook I'm using:Ī boat's crew rowed 16 kilometers downstream, with the current, in 2 hours. One problem I'm solving an investment problem involving two different interest rates, the next I'm solving the speed of a boat going down river versus its speed going upriver, and another problem I'm trying to find the number of nickels and dimes in a purse that adds up to $1.10.īonus question: How much information is too little? Or rather, what's the minimum amount of information needed to set up a problem as a linear system of equations? I'm having trouble identifying the common elements in them because the scenarios are so vastly different. I was solving various word problems such as mixing solutions, differing interest rates, boat speeds, etc., and I thought what's the common underlying factor among these problems which allow us to represent them as a system of linear equations?

Linear equation systems word problems