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26. The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number with its digits reversed. What is the original number?

26. The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number with its digits reversed. What is the original number?

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.5: Systems Involving Nonlinear Equations
Problem 39PS
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17. 5x - 2y = 7 - 2x + 3y 6 18. 2x-y 3 y = 2x + 8 19. 4x – y = -13 x + 3y = -13 20. -4x + 9y = 41 5x-4y = -44 Write and solve a system of equations for each problem. 21. Find two numbers whose sum is 3147 and whose difference is 135. 22. Jay took 10 hr to travel a total of 1100 mi. He averaged 50 mi/hr in his car and 200 mi/hr in his small plane. How much time did he spend in each? 23. It takes Bryce and Caleb the same amount of time to row 6 mi upstream as it takes them to row 18 mi downstream. If their rowing rate in still water is 4 mi/hr, what is the rate of the current? 24. If it takes 5 hr for a plane to travel 1400 mi with the wind and 7 hr to make the return trip against the wind, find the wind speed and the plane's air speed. 25. The difference between a two-digit number and five times the sum of its digits is 18. If the tens digit is twice the units digit, what is the number? 26. The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number with its digits reversed. What is the original number? 27. Evelyn invested $8400 in a CD and $9600 in a money market account whose APY is 1% less than that of the CD. If she made $804 in interest last year, what is the rate of interest on each account? 28. Danielle has 87 nickels, dimes, and quarters whose total value is $10. If the number of nickels is seven fewer than the total number of dimes and quarters, how many of each type of coin does she have? 141
Transcribed Image Text:17. 5x - 2y = 7 - 2x + 3y 6 18. 2x-y 3 y = 2x + 8 19. 4x – y = -13 x + 3y = -13 20. -4x + 9y = 41 5x-4y = -44 Write and solve a system of equations for each problem. 21. Find two numbers whose sum is 3147 and whose difference is 135. 22. Jay took 10 hr to travel a total of 1100 mi. He averaged 50 mi/hr in his car and 200 mi/hr in his small plane. How much time did he spend in each? 23. It takes Bryce and Caleb the same amount of time to row 6 mi upstream as it takes them to row 18 mi downstream. If their rowing rate in still water is 4 mi/hr, what is the rate of the current? 24. If it takes 5 hr for a plane to travel 1400 mi with the wind and 7 hr to make the return trip against the wind, find the wind speed and the plane's air speed. 25. The difference between a two-digit number and five times the sum of its digits is 18. If the tens digit is twice the units digit, what is the number? 26. The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number with its digits reversed. What is the original number? 27. Evelyn invested $8400 in a CD and $9600 in a money market account whose APY is 1% less than that of the CD. If she made $804 in interest last year, what is the rate of interest on each account? 28. Danielle has 87 nickels, dimes, and quarters whose total value is $10. If the number of nickels is seven fewer than the total number of dimes and quarters, how many of each type of coin does she have? 141
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