Word problems by type(you may want to include other examples of each type)
Translation problems:
Five less than twice a number is – 19. Find the number. Define a variable, write
an equation, solve, then answer the question in words.
The perimeter of a rectangle is 360 feet. The length of the rectangle is twice the width. Find the
length and width of the rectangle. Define a variable or variables, write an equation or system of
equations, solve, then answer the question in words.
The sale price of a cell phone is $45.99, which is 30% off the regular price. Find the regular price
of the cell phone. Round answer to the nearest cent, if necessary. Define a variable, write an
equation, solve, then answer the question in words.
The area of a rectangular slab of sidewalk is 45 ft2. Its length is 3 more than
four times its width. Find the length and width of the slab. Define a
variable, write an equation, solve, then answer in words.
The sum of the squares of two consecutive even integers in 100. Find the integers. Define a
variable, write an equation, solve, then answer the question in words.
Interest problem:
A new father is beginning to invest for his son’s college fund. He puts part of a $5000 account in a
fund that yields 7% annual interest and the rest is placed in a fund that yields 9% annual interest.
If he earns $380 in interest during the first year, how much is invested in each fund? Define a
variable or variables,write an equation or system of equations, solve, then answer the question in
words.
Principle Rate =Interest
1st account
2nd account
Mixture problem:
A 10% salt solution is to mixed with a 15% salt solution to produce 10 gallons of a 13% salt solution.
How many gallons of the 10% and how many gallons of the 15% solution will be needed? Define a
variable of variables, write an equation or system of equations, solve, then answer in words.
System of linear equation problem:
The income from a student production was $21,000. The price of a student ticket was $3 and non-
student tickets were $5 each. Five thousand people attended the production. How many tickets of
each kind were sold? Define a variable or variables, write an equation or system of equations, solve,
then answer in words.
Describe:X=______, Y=______
Equation 1:
Equation 2:
Proportion problem:
On a map, two cities are inches apart. If inches represents 30 miles, find the number of miles
between the two cities. Define a variable, write an equation, solve, then answer the question in words.
Uniform motion problems in terms of distance:
If a plane flying from an airport travels west at 550 mph and another leaving the same airport at the
same time travels east at 450 mph, in how many hours will the planes be 2600 miles apart? Define a
variable, write an equation, solve, then answer the question in words.
When Dewayne drives his car to work, the trip takes 30 min. When he rides the bus, it takes 45 min. The average speed of the bus is 12 mph less than his speed when driving. Find the distance he travels to work.
System of linear equations type:
A jet plane flying with the wind went 2100 mi in 4 hr. Against the wind, the plane could fly only 1760 mi in the same amount of time. Find the rate of the plane in calm air and the rate of the wind.
upstream
downstream
Uniform motion problems in terms of time:
The president of a company traveled 1800 mi by jet and 300mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 5 hours.
DistanceRate
One car travels 290 miles in the same amount of time it takes a second car traveling 5 miles per
hour faster than the first to go 315 miles. What are the speeds of the cars? Define a variable,
write an equation, solve, then answer the question in words.
DistanceRate
On a recent trip, a trucker traveled 330 mi at a constant rate. Because of road conditions, the trucker then reduced the speed by 25 mph. An additional 30 mi was traveled at the reduced rate. The entire trip took 7 hours. Find the two speeds
DistanceRate
Current type in terms of time:
A boat travels at a speed of 20 mph in calm water. It travels 48 miles upstream andthen returns to
the starting point in a total of 5 hours. Find the speed of the current.
DistanceRate
Rate problems
With the cold water valve open, it takes 8 minutes to fill a washing machine tub. With both the hot
and cold water valves open, it takes 5 minutes to fill the tub. How long will it take to fill the tub with
only the hot water valve open?
Rate 1:rate 2 :rate together:
b) Rate together = +
Tom can mow a lawn in 40 minutes and Walt can mow the same lawn in 30 minutes. How long
would it take the two of them working together to mow the lawn? Define a variable, write an
equation, solve, then answer the question in words.
Rate 1:rate 2 :rate together:
b) Rate together = +