Problem Solving
Estimating unknown quantities, picking the operations, converting units and folding in geometry to attack messy questions with trade-offs and no single answer.
33 exercises
Exercise 1
Determine which operation(s) you would use for each situation. There may be more than one correct answer.
The number of buses needed for a field trip.
How much you spend on groceries in a year.
Exercise 2
Determine which operation(s) you would use for each situation. There may be more than one correct answer.
The number of college credits you have left to take before transferring.
The number of months it will take to pay off a credit card.
Exercise 3
Estimate a reasonable range of values for each situation.
The number of steps to walk around a city block.
The number of soda cans that will fit in a large garbage bag.
Exercise 4
Estimate a reasonable range of values for each situation.
The distance from Portland, Oregon to New York City in miles.
The number of servings in a standard cereal box.
Exercise 5
Use a combination of operations to solve these problems. Document your steps and thinking.
You earn a weekly salary of $550 and $10 for each item after you sell 20 items in a week. How much will you earn if you sell 41 items this week?
Exercise 6
Use a combination of operations to solve these problems. Document your steps and thinking.
You earn a monthly salary of $2100 and $12 for each item after you sell 50 items in a month. How much will you earn if you sell 130 items this month?
Exercise 7
Use a combination of operations to solve these problems. Document your steps and thinking.
You are selling sandwiches for $10 each and your cost is $45 per dozen sandwiches. Find the profit on 120 sandwiches.
Exercise 8
Use a combination of operations to solve these problems. Document your steps and thinking.
You are selling lemonade for $3 each and your cost is $12.50 for 10 servings. Find the profit on 80 servings of lemonade.
Exercise 9
Use a combination of operations to solve these problems. Document your steps and thinking.
You ordered 50 shirts that you plan to sell for $18 each at an event. The cost was $9 per shirt. You sold 43 shirts and returned the rest but had to pay a $2 restocking fee on each shirt returned. What is your profit?
Exercise 10
Use a combination of operations to solve these problems. Document your steps and thinking.
You ordered 70 hats that you plan to sell for $20 each at an event. The cost was $8 per hat. You sold 65 of them and returned the rest but had to pay a $3 restocking fee on each hat returned. What is your profit?
Exercise 13
Use the problem solving process to decide between the two options. Document your steps and thinking.
You have two job offers. One pays a salary of $60,000 per year. The other job pays $28 per hour for 40 hours a week with a $500 signing bonus. If the jobs and benefits are similar, which job would you choose?
Exercise 14
Use the problem solving process to decide between the two options. Document your steps and thinking.
You have two job offers. One pays a salary of $85,000 per year with a $2,000 yearly bonus that has the possiblity to increase. The other job pays $42.50 per hour for 40 hours a week. If the jobs and benefits are similar, which job would you choose?
Exercise 15
Use the problem solving process to decide between the two options. Document your steps and thinking.
In this exercise, if the hourly job had overtime pay at time and a half, how many hours of overtime per year would you need to work in a year to get paid as much as the salaried job?
Exercise 16
Use the problem solving process to decide between the two options. Document your steps and thinking.
In this exercise, how much would the yearly bonus in the salaried job need to be for you to get paid as much as the hourly job?
Exercise 17
Use the problem solving process to decide between the two options. Document your steps and thinking.
You are organizing a large dinner event. One venue charges $155 per person and you have a prior credit of $4,600. Another venue charges $500 per table of 8 people. Which venue is more cost effective?
Exercise 18
Use the problem solving process to decide between the two options. Document your steps and thinking.
You are organizing a large dinner event. One venue charges $950 per table of 12. Another venue charges a setup fee of $1500 and $40 per person. Which venue is more cost effective?
Exercise 19
Use unit coversions and/or geometric formulas to solve these problems as needed. Document your steps and thinking.
You are in charge of drinks for a neighborhood block party. You need at least 100 cups of beverages. So far, you have received enough mix to make 3 gallons of lemonade and 6 bottles of fruit juice that each contain are 32 fl. oz. How many cups of beverage do you have so far? Is this en…
Exercise 20
Use unit coversions and/or geometric formulas to solve these problems as needed. Document your steps and thinking.
You are in charge of drinks for a community barbecue. You need at least 150 cups of beverages. So far, you have received enough mix to make 20 quarts of punch and 9 2-L bottles of soda. How many cups of beverage do you have so far? Is this enough for the block party?
Exercise 21
Use unit coversions and/or geometric formulas to solve these problems as needed. Document your steps and thinking.
A pediatrician prescribes 0.5 mg/kg/day of a medication. If the child weights 33 pounds, how many milligrams do they need? If the chewable tablets come in 2.5 or 3.5 mg, which ones should be purchased and how many tablets should be given?
Exercise 22
Use unit coversions and/or geometric formulas to solve these problems as needed. Document your steps and thinking.
A doctor prescribes 5 mg of medication per kilogram of body weight. If a patient weighs 154 pounds, how much medication should they receive in milligrams? If tablets are 50 mg each, how many tablets should they take?
Exercise 23
Use unit coversions and/or geometric formulas to solve these problems as needed. Document your steps and thinking.
Parvina wants to fill her 2 rectangular raised garden beds, which are 6 feet long, 3 feet wide, and 1.5 feet deep. If bags of soil contain 2 cubic feet, how many bags does she need to buy?
Exercise 24
Use unit coversions and/or geometric formulas to solve these problems as needed. Document your steps and thinking.
Sidiki wants to fill a circular sandbox with a diameter of 5 feet and a depth of 1.5 feet. If bags of sand contain 3 cubic feet each, how many bags does he need to buy?
Exercise 25
Use the problem solving process to solve these problems. For this set of questions, after you identify the information you need, click on the link in the question or go to Information for Problem Solving Problems to find that information. The details may be imprecise; answer the question the best you can with the provided information. Document your steps and thinking.
You’re planning on making 6 me…
Exercise 27
Use the problem solving process to solve these problems. For this set of questions, after you identify the information you need, click on the link in the question or go to Information for Problem Solving Problems to find that information. The details may be imprecise; answer the question the best you can with the provided information. Document your steps and thinking.
You need to buy some chicken f…
Exercise 28
Use the problem solving process to solve these problems. For this set of questions, after you identify the information you need, click on the link in the question or go to Information for Problem Solving Problems to find that information. The details may be imprecise; answer the question the best you can with the provided information. Document your steps and thinking.
I have an old gas furnace, and…
Exercise 29
Use the problem solving process to solve these problems. For this set of questions, after you identify the information you need, click on the link in the question or go to Information for Problem Solving Problems to find that information. The details may be imprecise; answer the question the best you can with the provided information. Document your steps and thinking.
Janine is considering buying a…
Exercise 30
Use the problem solving process to solve these problems. For this set of questions, after you identify the information you need, click on the link in the question or go to Information for Problem Solving Problems to find that information. The details may be imprecise; answer the question the best you can with the provided information. Document your steps and thinking.
Marcus is considering going ca…
Exercise 31
Use the problem solving process to solve these problems. For this set of questions, research or make educated estimates for any unknown information needed to answer the question. Document your steps and thinking.
You want to travel from Portland, OR to San Francisco, CA for a wedding. Compare the costs and time involved with driving, flying, and taking a train. Assume that if you fly or take the tr…
Exercise 32
Use the problem solving process to solve these problems. For this set of questions, research or make educated estimates for any unknown information needed to answer the question. Document your steps and thinking.
You want to paint the walls of a 6ft by 9ft storage room that has one door and one window. You want to put on two coats of paint. How many gallons and/or quarts of paint should you buy to…
Exercise 33
Use the problem solving process to solve these problems. For this set of questions, research or make educated estimates for any unknown information needed to answer the question. Document your steps and thinking.
A restaurant in New York tiled their floor with pennies. Just for the materials, is this more expensive than using a more traditional material like ceramic tiles? If each penny has to be l…
Exercise 34
Use the problem solving process to solve these problems. For this set of questions, research or make educated estimates for any unknown information needed to answer the question. Document your steps and thinking.
You are considering taking up part of your back yard and turning it into a vegetable garden, to grow broccoli, tomatoes, and zucchini. Will doing so save you money, or cost you more than b…
Exercise 35
Use the problem solving process to solve these problems. For this set of questions, research or make educated estimates for any unknown information needed to answer the question. Document your steps and thinking.
Barry is trying to decide whether to keep his 1993 Honda Civic with 140,000 miles, or trade it in for a used 2008 Honda Civic. Consider gas, maintenance, and insurance costs in helping him…
Exercise 36
Use the problem solving process to solve these problems. For this set of questions, research or make educated estimates for any unknown information needed to answer the question. Document your steps and thinking.
Some people claim it costs more to eat vegetarian, while some claim it costs less. Examine your own grocery habits, and compare your current costs to the costs of switching your diet (from…
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