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89.three times5.First, determine the unknowns. Let xthe larger number and ythe smaller number.==The question asks us to find the value of the larger number and the value of the smaller number. These are the unknownvalues, 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 writethe smaller number" in terms of a variable as three times5.""three times3y.The second equation of the system is written below.x − 3y = 5We now have the following system of equations in two unknowns.x + y = 89x − 3y = 5Now, 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.− 1Multiply the second equation by .− 1( − 1)(x − 3y)=(5)( − 1)− x + 3y =− 5We now have the following equivalent system of equations, which can be added together to eliminate the x terms.x +y=89− x + 3y=− 5y4=84Divide by to solve for y.4y4=84y=21Now find the value of x. Substitute the value found for y into the first equation from the original system of equations.x + y=89x + 21=89x=68Therefore, 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.6821Practice for the Final Exam: Chapter 4 Review-Barone Morales1 of 14/1/2016 2:31 AM
Student: Barone MoralesDate: 4/1/16Instructor: Carl LetscheCourse: MATH110 D012 Win 16Assignment: Practice for the FinalExam: Chapter 4 ReviewPractice for the Final Exam: Chapter 4 Review-Barone Morales1 of 24/1/2016 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.159113Read and reread the problem. LetAthe price of an adult's ticket=Cthe price of a child's ticket=We translate the problem into two equations using both variables.In words:Three Adultsandfour childrenmust pay159Translate:3A+4C=159In words:Two adultsandthree childrenmust pay113Translate:2A+3C=113Now solve the system.3A + 4C = 1592A + 3C = 113Since 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 follows2()simplifies to 3A + 4C = 1596A + 8C = 3183() simplifies to−2A + 3C = 113− 6A − 9C = − 339Next, add the two equations.