Bailey is planting an outdoor garden. She wants the length of the planting area to be twice as large as the width. If she has 128 square feet of soil to work with, what dimensions must the garden be?
Word problems are some of the hardest types of problems for students to grasp. There are a few steps to solving any word problem:
- Read the problem at least twice.
- Cross out any unnecessary words, circle any numbers or words that represent mathematical operators, or translate words into mathematical expressions.
- Write an equation and solve.
To help you with steps 2 and 3, generate a list of words that represent: add, subtract, multiply, divide, equal, etc. Here are a few to get you started.
sum plus and
increase more (than)
times of product
double (x2) triple (x3)
decrease less (than)
is total to
quotient half (÷2)
how many __
how much __
what amount (of) __
See if you can add anything to these lists. Then, use this chart to help you with decoding word problems.
Two consecutive numbers add up to 55. What are the two numbers?
Over the Winter Break, you worked at a clothing store and made $9.00 an hour. For the two weeks you worked 65 hours of regular pay and 10 hours of overtime (time and a half). How much money did you make?
Elise is taking piano lessons. The first lesson is twice as expensive as each additional lesson. Her mom spends $270 for 8 lessons. How much was the first lesson?
Solution:Translate each statement.
The regularly priced lessons are $30. The first lesson will be $60.
1. Bob is twice as old as his daughter. In that same year, his granddaughter is one-tenth his daughter's age. His granddaugther is 3. How old is Bob?
2. Javier needs to get a tank of gas. Gas costs $3.79 per gallon. How much money does Javier need to fill up his 16 gallon tank?
1. Rewrite each statement as a mathematical one.
Now, plug in the granddaughter's age and work through each equation.
Bob is 60 years old.
Answer each question to the best of your ability.
- The average speed on highway 101 is 65 miles per hour (mph). Assuming you drive the speed limit, how long will it take you to drive 350 miles? Use the formula distance=rate⋅time. Round your answer to two decimal places.
- Using the information in #1, how many miles did you drive on highway 101 if you drove for 2.5 hours?
- The sum of two consecutive numbers is 79. Find the two numbers.
- The sum of two consecutive odd numbers is 44. Find the two odd numbers.
- You borrowed $350 from your parents for a new Wii and games. They are not going to charge you interest, but you need to pay them back as quickly as possible. If you pay them $15 per week, how long will it take you to pay them back?
- George is building a rectangular, fenced-in dog run. He has 120 feet of fencing and wants the length to be 20 feet greater than the width. If you use all the fencing, find the length and width of the dog run.
- Cynthia is selling chocolate bars for a fundraiser for school. Each bar costs $1.50. If she needs to raise $225, how many chocolate bars does she need to sell?
- Harriet bakes and sells cookies to local stores. Her cost for one dozen cookies is $2.75 and she sells them to stores for $7.00 (per dozen). How many dozen cookies does she need to make to earn $500? Round to the nearest dozen.
- A football field is a rectangle where the length is 100 yards. If the total perimeter is 1040 feet, what is the width of a football field? Leave your answer in feet.
Challenge The sum of three consecutive even numbers is 138. What are the three numbers?