Section 3.4 Applications of Systems of Linear Equations in Two Variables 261 Answer 1. Soft drinks cost $2.50 and popcorn costs $4.00. Solving a Cost Application Example 1 At an amusement park, five hot dogs and one drink cost $22. Two hot dogs and three drinks cost $14. Find the cost per hot dog and the cost per drink. Concepts 1. Applications Involving Cost 2. Applications Involving Mixtures 3. Applications Involving Principal and Interest 4. Applications Involving Uniform Motion 5. Applications Involving Geometry Applications of Systems of Linear Equations in Two Variables Section 3.4 1. Applications Involving Cost In Chapter 1 we solved numerous application problems using equations that contained one variable. However, when an application has more than one unknown, sometimes it is more convenient to use multiple variables. In this section, we will solve applications containing two unknowns.When two variables are present, the goal is to set up a system of two independent equations. Solve for d in the first equation. Substitute the quantity for d in the second equation. Clear parentheses. Solve for h. 5h 22 Substitute h 4 in the equation d 5h 22. Solution: Let h represent the cost per hot dog. Label the variables. Let d represent the cost per drink. Write two equations. aCost of 5 hot dogs aCost of 2 hot dogs b acost of 1 drink b acost of 3 drinks b $22 5h d 22 b $14 2h 3d 14 This system can be solved by either the substitution method or the addition method.We will solve by using the substitution method.The d variable in the first equation is the easiest variable to isolate. 5h d 22 d 5h 22 2h 3d 14 2h 315h 222 14 2h 15h 66 14 13h 66 14 13h 52 h 4 d 5142 22 d 2 Because h 4, the cost per hot dog is $4.00. Because the cost per drink is $2.00. d 2, Skill Practice 1. At the movie theater,Tom spent $15.50 on 3 soft drinks and 2 boxes of popcorn. Carly bought 5 soft drinks and 1 box of popcorn for a total of $16.50. Use a system of equations to find the cost of a soft drink and the cost of a box of popcorn.
miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above