Applied Problems: Mixture and Money By Mr. Richard Gill Dr. Marcia Tharp Tidewater Community College Click to view.

Introduction We are going to use a six- step process for solving Mixture and Money Problems. The steps are: 1) Read the problem. 2) Define x. 3) Name the unknown quantities in terms of x. 4) Form an equation. 5 ) Solve the equation. 6) Check to see if you answered the question. Now lets go on and see how this works in a problem.

Example 1 Print this page. The Hurrah Players sold 600 tickets to a recent event. Adults paid $5 each and students paid $2 each. If the total collected was $2025, how many tickets of each type were sold?

2. Define x. Let x answer the question. In other words, let x equal the number of adult tickets sold. x= the number of adult tickets. (It would be OK to let x equal the number of student tickets but, of course, x cannot be both things simultaneously. It is very important to write down your definition of x so that you don’t get lost in your own problem.) 1. 1.Read the problem. A casual guess might be 250 adult and 350 student tickets.

3. Name other unknown quantities in terms of x. This is usually the crucial step in the solution. In money problems, it is very important to remember that the number of tickets and the value of the tickets are two different quantities. 600 – x = the number of student tickets. 5x = the amount of money from adult tickets ($5 per ticket) 2(600 – x) = the amount of money from student tickets

4. Form the equation. The money from the student tickets and the money from the adult tickets should add up to equal the total amount collected. cost student tickets + cost adult tickets = total collected 5x + 2(600 – x) = 2025

5. Solve the equation. 5x + 2(600 – x) = x – 2x = x = 825 x = 275

6. Answer the question. We have answered the first part of the question since we defined x as the number of adult tickets sold. To find the number of student tickets sold we need only to calculate the value of 600 – x. x = 275 the number of adult tickets sold 600 – x = 325 the number of student tickets sold = 375

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Applied Problems: Motion Example 2 Motion problems use the equation D = RT where D is the distance traveled, R is the rate of travel and T is the time spent traveling. It is helpful to use a D = RT grid when solving motion problems as shown in the following example.

Juan and Amal leave DC at the same time headed south on I-95. If Juan averages 60 mph and Amal averages 72 mph how long will it take them to be 30 miles apart? Now would be a good time for a guess. Write yours down and compare it to the answer you get algebraically. RateTimeDistance Juan60 x60x Amal72 x72x

The purpose of the grid is to find an algebraic name for each distance. Notice that the distance 30 miles does not appear in the grid because neither Juan nor Amal traveled 30 miles. Notice also that we could use x for each time since Juan and Amal were on the road for the same amount of time. We will need to work 30 miles into the equation as follows: RateTime Distance Juan60x60x Amal72x72x Juan’s distance – Amal’s distance = 30 miles 72x – 60x = 30 12x = 30 x = 2.5 hrs.

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