Miscellaneous Problems

Mathematical problem solving skills can be important in everyday life.

True

Use the three steps to solve the problem. The length of a rectangle is 2 inches less than 3 times the number of inches in its width. If the perimeter of the rectangle is 28 inches, what is the width and length of the rectangle?

Width - 4 Length - 10

A purse contains 21 coins consisting of nickels and dimes. Find the number of coins of each kind if the total value is $1.65. If 5n represents the value of the nickels, then which of the following expressions represents the value of the dimes?

10(21 - n)

Use the three steps to solve the problem. One number is 11 more than twice another number. If the sum of the numbers is twice their difference, find the numbers.

11, 33

Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement. If x represents the measure of the angle, then which of the following expressions would equal x?

0.5(90 - x) - 18

The length of a rectangle is 3 times its width. If the length were increased by 2 inches and the width by 1 inch, the new perimeter would be 62 inches. What is the width and length of the rectangle? If w represents the width of the rectangle, then which equation could be used to solve for w?

2(4w + 3) = 62

For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations. If she has 22 travelers checks in all, how many of each denomination does she have? Let x represent the number of $10 traveler's checks she has. Which expression represents the value of the $20 traveler's checks she has?

20(22 - x)

The successor of a certain number when added to twice the number produces 61. What is the number? If n represents the number, which equation could be used to solve for n?

2n + n + 1 = 61

Mac and his brother Ted collect coins. Mac's collection contains 8 more than twice as many as Ted's. If the total number of coins in the two collections is 74, how many coins are in each collection? If x represents the number of coins in Ted's collection, then which expression represents the number of coins in Mac's collection?

2x+8

The capacities of two trucks are 3 tons and 4 tons respectively. If the smaller truck makes 18 more trips than the larger, it can deliver 12 more tons of freight than the larger. How many trips does each truck make? Let x represent the number of trips that the larger truck makes. Which of the following equations could be used to solve the problem?

3(x + 18) - 4x = 12

The perimeter of a rectangle is 256 inches. How long are the sides if the length exceeds the width by 16 inches? Mark lets x represent the width of the rectangle and writes the equation 2x + 2(x + 16) = 256. Solving for x, the width of the rectangle is

56

How many pounds of cashew nuts worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to make a mixture worth $1.00 a pound? Which of the equations could be used to solve for p, the pounds of cashew nuts?

75p + 150(10) = 100(p + 10)

Use the three steps to solve the problem. Mrs. West is 14 years younger than her aunt. If Mrs. West's age in years is as much below 60 as her aunt's age is over 40, how old is each?

aunt's age - 57 Mrs. West's age - 43

Use the three steps to solve the problem. Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50 gallons of the mixture?

maple syrup - 15 gallons corn syrup - 35 gallons