The sum of two numbers is 32 and their difference is 14. Find the numbers.

Equations :

Answer:9 and 23

206-T1

Three times a larger number added to four times a smaller number equals 44. The difference between two times the smaller number

and the larger number is two. Find the two numbers.

Equations :

Answer:5 and 8

206-T2

Four times a larger number added to twice a smaller number equals 58. The difference between nine times the smaller number and

three times the larger number is 30. Find the two numbers.

Equations :

Answer:Smaller number = 7, Larger number = 11

206-T3

One number is four times another number. The difference between three times the larger number and two times the smaller number is

20. Find the two numbers.

Equations :

Answer:Smaller number = 2, Larger number = 8

206-T4

The Malibu Department Store sells eight ties and seven shirts for $201. At the same time, the store sells nine ties and six shirts for

$183. Find the cost of one shirt and one tie.

Equations :

Answer:One shirt costs $23, one tie costs $5

206-T5

Helene’s sells four blouses and five skirts for $262. At the same time, the store sells seven blouses and four skirts for $278. Find the

cost of one blouse and one skirt.

Equations :

Answer:One blouse costs $18, one skirt costs $38

206-T6

The Village Book Store sells a total of 400 books a week. It makes a profit of $5 per each softcover book and $6 per each hardcover

book. The weekly profit is $2,080. How many softcover and hardcover books did the store sell?

Equations :

Answer:320 softcover books, 80 hardcover books

206-T7

The Ben Franklin Eyeglass Factory sells wire-frame eyeglasses and plastic-frame eyeglasses. They sell a weekly total of 250 eyeglasses

for a weekly profit of $2,88. If they make a profit of $12 on each wire-frame pair and a $9 profit on each plastic-frame pair, how

many eyeglasses of each type did they sell?

Equations :

Answer:210 wire-frame eyeglasses, 40 plastic-frame eyeglasses

206-T8

Jester invests some money at an annual rate of 7% and $4,000 more than this amount at an annual rate of 6%. If the total annual

return is $890, how much did he invest at each rate?

Equations :

Answer:$5,000 at 7%, $9,000 at 6%

206-T17

Jaqueta has $10,000 to invest. She puts some money in a mutual fund at an annual rate of 10% and the remainder into common

stocks paying an annual return of 7%. If her total annual income is $910, how much does she invest in each place?

Equations :

Answer:$7,000 in a mutual fund, $3,000 in common stocks

206-T19

Manfredo invests some money in real estate at an annual rate of 11% and $5,000 more than twice this amount in U.S. Treasury Bills

at an annual rate of 7%. If his total annual return is $,100, how much does he invest in each place?

Equations :

Answer:$15,000 in real estate, $35,000 in U.S. Treasury Bills

206-T18

The X Corporation has $50,000 to invest. It places some money into Turkish bonds at an annual rate of 12% and the remainder into

British bonds paying an annual interest rate of 9%. If the annual return on the British bonds was $2,610 more than the annual return

on the Turkish bonds, how much was invested in each place?

Equations :

Answer:5 square centimeters

208-T20

A sailboat can travel at the rate of 40 mph in still water. Together with a current, it can move 368 miles in the same time that it can

move 272 miles against the current. Find the current speed.

Equations :

Answer:6 mph

206-T9

An airplane flies 4,340 miles against the wind in seven hours and 4,080 miles in six hours with the wind. Find the speed of the

airplane.

Equations :

Answer:650 mph

206-T10

A Mississippi steamboat travels downstream a distance of 240 miles in eight hours. If it can travel the same distance upstream in 10 hours, find the rate of the current and the rate of the boat in still

water.

Equations :

Answer:Rate of the current is 3 mph, rate of the boat is 27 mph

206-T11

The Whale, tugboat, can move 40 miles in 10 hours against the current. If it can cover the same number of miles downstream in 4

hours, find the rate of the current.

Equations :

Answer:3 mph

206-T12

In a two-digit number, the sum of the digits is 12 and the difference is six. If the tens’ digit is larger, what is the two-digit number?

Equations :

Answer:93

206-T13

In a two-digit number, three times the tens’ digit added to five times the units digit equals 53. The difference between four times the tens’ digit and two times the units’ digit is 10. What is the two-

digit number?

Equations :

Answer:67

206-T14

In a two-digit number, the difference between eight times the tens’ digit and three times the units’ digit is 11. At the same time, the difference between five times the units’ digit and two times the

tens’ digit is 27. Find the two-digit number.

Equations :

Answer:47

206-T15

In a two-digit number, the sum of the digits is 10. If the digits are reversed, the new number is 18 less than the original number. What

was the original number?

Equations :

Answer:64

206-T16