Application of Systems of Equations

The sum of the digits of a two digit number is 14. The difference between the tens digit and the units digit is 2. If x is the tens digit and y is the ones digit, which system of equations represents the word problem?

x + y = 14 and x - y = 2

One number is twice another number and their sum is 36. Which system of equations represents the word problem?

x + y = 36 and y = 2x

A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66? If x represents the number of 13 cent stamps and y the 18 cent stamps, which system represents the problem?

x + y = 42 and 0.13x + 0.18y = 6.66

The sum of two numbers is 62 and their difference is 16. Which system of equations represents the word problem?

x + y = 62 and x - y = 16

Solve this problem by using a two order system. A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate?

$ 3,800 at 4% and $1,400 at 3%

Solve this problem by using a two order system. A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66?

24 18

Use the three steps to solve the problem. With a certain tail wind a jet aircraft arrives at its destination, 1,890 miles away, in 3 hours. Flying against the same wind, the plane makes the return trip in 3 3/8 hours. Find the wind speed and the plane's airspeed.

35 595

Which of the following are steps in the process in solving application problems using the two-order system?

Assign two variables for the unknowns. Write two equations using the assigned variables. Solve the pair of equations.

Mr. Rose spent $63 for a sport jacket and a pair of slacks. If the jacket cost $33 more than the slacks, how much did he pay for each? Which system of equations represents the word problem if j is the jacket price and s is the price of the slacks?

j + s = 63 and j - s = 33

The sum of two consecutive numbers is 77. The difference of half of the smaller number and one-third of the larger number is 6. If x is the smaller number and y is the larger number, which two equations represent the sum and difference of the numbers?

x + y = 77 and 1/2 x - 1/3 y = 6

One of two complementary angles is 8 degrees less than the other. Which of the following systems of equations represents the word problem?

x + y = 90 and x - y = 8

The larger of two numbers exceeds twice the smaller by one. Three times the smaller exceeds the larger by six. If y is the larger number, which of the following systems of equations represents the word problem?

y = 2x + 1 and y + 6 = 3x

One number is 3 more than another and their sum is 41. Which of the following systems of equations represents the word problem?

y = x + 3 and x + y = 41

John is 5 years older than Mary. In 10 years, twice John's age decreased by Mary's age is 35, and John's age will be twice Mary's current age. Find their ages now. If x is Mary's age now and y is John's age now, which system of equations could not be used to solve the problem?

y = x + 5 and 2(y + 10) = x