89. three times 5. First, determine the unknowns. Let x the larger number and y the smaller number. = = The question asks us to find the value of the larger number and the value of the smaller number. These are the unknown values, so we set up the variables to represent these values. Next, since there are two variables, write a system of equations in the two unknowns. Start with the statement, "The sum of two numbers is We write this in terms of the variables as 89." x + y = 89. Now, look at the statement, "If the smaller number is subtracted from the larger number, the result is We write the smaller number" in terms of a variable as three times 5." "three times 3y. The second equation of the system is written below. x − 3y = 5 We now have the following system of equations in two unknowns. x + y = 89 x − 3y = 5 Now, solve the system. We can eliminate the x terms from the system by multiplying the second equation by and then adding it to the first equation. − 1 Multiply the second equation by . − 1 ( − 1)(x − 3y) = (5)( − 1) − x + 3y = − 5 We now have the following equivalent system of equations, which can be added together to eliminate the x terms. x + y = 89 − x + 3y = − 5 y 4 = 84 Divide by to solve for y. 4 y 4 = 84 y = 21 Now find the value of x. Substitute the value found for y into the first equation from the original system of equations. x + y = 89 x + 21 = 89 x = 68 Therefore, the larger number is and the smaller number is . These values can be substituted into the second equation in the original system as a check. 68 21 Practice for the Final Exam: Chapter 4 Review-Barone Morales 1 of 1 4/1/2016 2:31 AM
Student: Barone Morales Date: 4/1/16 Instructor: Carl Letsche Course: MATH110 D012 Win 16 Assignment: Practice for the Final Exam: Chapter 4 Review Practice for the Final Exam: Chapter 4 Review-Barone Morales 1 of 2 4/1/2016 2:31 AM
Jen Butler has been pricing Speed-Pass train fares for a group trip to Washington D.C. Three adults and four children must pay $ . Two adults and three children must pay $ . Find the price of the adult's ticket and the price of a child's ticket. 159 113 Read and reread the problem. Let A the price of an adult's ticket = C the price of a child's ticket = We translate the problem into two equations using both variables. In words: Three Adults and four children must pay 159 Translate: 3A + 4C = 159 In words: Two adults and three children must pay 113 Translate: 2A + 3C = 113 Now solve the system. 3A + 4C = 159 2A + 3C = 113 Since both equations are in standard from, we solve by the addition method. First we multiply the first equation by 2 and the second equation by 3 so that when we add the equations we eliminate the variable A. − After the multiplication, the system is as follows 2( ) simplifies to 3A + 4C = 159 6A + 8C = 318 3( ) simplifies to − 2A + 3C = 113 − 6A − 9C = − 339 Next, add the two equations.
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