Word Problems

Question 1

What is active reading when applied to SAT Math?

Answer 1

Active reading is:

• reading for keywords/terms
• reading for value details
• reading to find connection to formulas or concepts
• reading for traps
• reading to apply problem solving

Question 2

What are the most common types of word problems on the SAT math test?

Answer 2

• distance problems
• age problems
• percentage problems
• number problems
• mixture problems
• work problems

Question 3

What are the simple techniques you should practice to train yourself to read actively?

The average of three consecutive odd integers is 93. What would the GREATEST of these integers equal?

Answer 3

* Read with the pencil over the word you’re focusing on

• Define all terms (average, consecutive, odd, integers, greatest)
• Project terms into examples (1,3,5)
• Mark significant value details (3, 91)
• Make connections to formulas (93=total/3)
• Find traps (GREATEST - attention to detail trap)

Question 4

What should you recognize about a word problem as you begin to read it actively?

Mary is three times as old as her sister Carry, who is five years older than their cousin Jessy. If in 15 years Mary will be twice as old as Jessy will be then, how old is Carry?

Answer 4

Recognize type of problem.

This is an age problem. You should realize that translating the information into number sentences can get tricky here. So, do it slowly.

Question 5

How should you reduce the information of this word problem into number expressions?

Mary is three times as old as her sister Carrie, who is five years older than their cousin Jessie. If in 15 years Mary will be twice as old as Jessie will be then, how old is Carrie?

Answer 5

Read. Stop and Think.

“Mary is three times as old as Carrie”

So, m = c

(think: where does the “three” go. Mary could be 9 and Carrie 3, which means they are equal when you multiple Carrie’s age by three) so,

m = 3c

“Carrie…is five years older than Jessie”

So, c = j

(think: where does the +5 go. Carrie could be 10 and Jessie could be 5. Threrefore they are equal when we add 5 to Jessie) so,

c = j + 5

“In fifteeen years…”

(think: everyone is +15 years) so

m +15 = j + 15

“mary will be twice as old as Jessie”

(think: where does the “twice” go. Mary could be 30 and Jessie 15. Therefore Jessie times two is equal to Mary) so

m + 15 = 2(j + 15)

Now you have three statements for your three variables, and you can solve

Question 6

What information should you underline in this word problem as you read it?

Today, Anne is twice as old as Mike, but three years ago, she was two years older than Mike is now. How old is Mike now?

Answer 6

• “twice”
• “three years ago”
• “now”

Question 7

After reading and mapping the word problem, what’s the first step in problem solving?

Answer 7

Identifying the type of problem will help trigger your brain to think of the approach and any formula you’ll need. This is often the work of a nanosecond.

Question 8

What type of word problem is this….?

If a factory produces 3,000 plastic forms in h hours, how many plastic forms can it produce in m minutes?

(a) ^m/_50<em>h</em>
(b) 50hm
(c) ^<em>hm</em>/₅₀
(d) ^50<em>m</em>/_h
(e) ^50<em>h</em>/_m

Answer 8

It’s a production rate problem. The formula is essentially the same as for distance.

Production rate = ^{things done}/_time

or r = ^u/_t

things done = 3,000 units. Time = h. ⇒ p = ^3,000/_h.

Question 9

Can you identify the type of the following word problem?

If John is as old as Michael and Rowan equal to the sum of Michael’s age and twice Rowan’s age, what is the average age of John and Michael?

Answer 9

This is an age word problem.

There is no specific formula to remember. To successfully solve age word problems, your goal is to recognize who and pick variables to stand for the unknows. Name and label clearly so you know what exactly they stand for. Set up an equation based upon information.

Question 10

Identify the type of question and connect to the formula necessary to set up the problem.

A driver, travelling at a constant rate reaches work one hour after departing from home, and returns by the same route at 10 miles per hour greater than his earlier rate. At what rate did he drive to work?

Answer 10

This is a DRT problem. Since the route to and from work is equal, the problem sets up this way:

R_w * T_w = R_h * T_h

R_h = R_w + 10

Question 11

How should you approach the following type of question?

Ellen is making twenty pancakes for six friends. The amount of required pancake mix is proportional to the number of pancakes that are being made. The recipe calls for 1 cup of mix and three-quarters of a cup of water to make 8 pancakes. How many cups of water does Ellen need in order to make enough pancakes for her hungry friends?

Answer 11

This is a mixture word problem. On these kinds of questions, you should be:

1. Do this first
2. This second
3. this third

Solution to sample problem:

Question 12

You run 2 miles in 10 minutes, at a constant speed. How many feet do you run in 30 seconds?

*** 1 mile = 5,280 feet

Question 13

Laura makes 5% more than Jim. If this year, Jim gets a $1,500 raise, their salaries would become equal. How much money does Jim earn a year?

Answer 13

Diagram:

L: 5% > J

J: $1500 raise

L = J

J + 1500 = L

L = 1.05*J

30,000

Question 14

The sum of Mary’s age and Simon’s age is 12. The product of their ages is 32. What is the difference between their ages?

Answer 14

4

M + S = 12

M x S = 32

Question 15

In a 4-digit number, the sum of all digits is 12. The sum of my first and third digits equals its last digit. The third digit is 60% of the last digit. What is that 4-digit number?

Answer 15

2,235

The last digit is 5. That’s the only digit 60% of which would give you a whole number. The third digit is 3. The first digit is 2. Therefore, the second digit is 2.

Question 16

How would you diagram the following speed word problem?

You decided you needed exercise and walked from school to the mall at an average speed of 4 mph. Your friend left the school 45 minutes later but rode a bike to the mall. His speed was 8 mph. If the distance between the school and the mall is 6 miles, will your friend catch you on the way? if yes, in how many hours/minutes?

Answer 16

Once you you have actively read and identified the type of word problem, it’s time to diagram.

For this speed word problem, you might use the following diagram:

Question 17

Total of 4,950 pounds of tomatoes were harvested on two different farms. The first farm packed them in 20-pound boxes. The second farm packed tomatoes in 30-pound boxes. How many pounds of tomatoes did each farm collect if there were 10 more of heavier (30-pound) boxes?

Answer 17

You should be thinking:

1. Step 1
2. Step 2
3. Step 3

Solution:

Question 18

The distance around a track field is 600 meters. Lizzy runs around the field 6 times in three-quarters of an hour. What is her average speed in meters per minute?

Question 19

Alex, Chris and John save money to buy concert tickets. The amount of money that Alex and Chris have is $125. The amount of money that Chris and John have is $95. The amount of money that Alex and John have is $100. How much money do three of them have in total?

Question 20

Two electricians need to check 150 electrical units. One can do this job in 15 days, the other one can do it in 10 days. If they work together, how many days would be required to complete the job?

Question 21

One tank has three times as much water as the other one. The first tank was filled with additional 46 liters of water, while only 18 liters were added to the second tank. Both tanks now contain 184 liters of water. How many liters of water did each tank contain originally?

Question 22

Two boats leave the pier going in the opposite directions. The speed of the first boat is 25 mph. What will be the distance between them after 4 hours if the second boat was 48 miles from the pier after two hours?

Question 23

Two trains leave town A and town B respectively moving towards each other. The distance between A and B is 777 miles. The first train departed 3 hours ealier than the second train, going at a constant rate of speed of 75 mph. The trains meet in 4 hours after the departure of the second train. What is the speed of the second train?

Question 24

A certain company needs 1,200 brochures for a meeting. One printing shop can do the work in 3 days, the other shop will complete the work in 6 days. How many days would both shops need to finish the job working together?

Question 25

The ratio of gold beads to silver beads in a box was 7 : 4. After Sarah used 81 gold beads to make a necklace, the ratio of silver beads to gold beads became 10 : 13. How many beads of each color were in the box originally? How many beads of each color were left in the end?

Question 26

How would you map the following word problem?

A driver, setting off from New York City, gets to Boston in 5.5 hours. First 2.5 hours he drives at an average speed of 60 mph, then stops at a rest area for one-half hour. Realizing he is late, the driver increases the speed by 10% for the second part of the trip. What is the distance between New York City and Boston?

Answer 26

Draw a sort of number line to indicate a trip from point N (New York) to point B (Boston).

Question 27

How would you map the following word problem?

A driver, setting off from New York City, gets to Boston in 5.5 hours. First 2.5 hours he drives at an average speed of 60 mph, then stops at a rest area for one-half hour. Realizing he is late, the driver increases the speed by 10% for the second part of the trip. What is the distance between New York City and Boston?

Answer 27

Draw a sort of number line to indicate a trip from point N (New York) to point B (Boston).

Question 28

Step 1: How to Read Actively for the following question:

A driver, setting off from New York City, gets to Boston in 5.5 hours. First 2.5 hours he drives at an average speed of 60 mph, then stops at a rest area for one-half hour. Realizing he is late, the driver increases the speed by 10% for the second part of the trip. What is the distance between New York City and Boston?

Answer 28

On this question, to Actively Read, you highlight the key info

A driver, setting off from New York City, gets to Boston in 5.5 hours. First 2.5 hours he drives at an average speed of 60 mph, then stops at a rest area for one-half hour. Realizing he is late, the driver increases the speed by 10% for the second part of the trip. What is the distance between New York City and Boston?

Question 29

How would you map the following word problem?

A driver, setting off from New York City, gets to Boston in 5.5 hours. First 2.5 hours he drives at an average speed of 60 mph, then stops at a rest area for one-half hour. Realizing he is late, the driver increases the speed by 10% for the second part of the trip. What is the distance between New York City and Boston?

Answer 29

Draw a sort of number line to indicate a trip from point N (New York) to point B (Boston).

Question 30

The cost of a telephon call using a carrier A is $1.00 for any time up to and including 20 mins and $0.07 per minute thereafter. The cost using long-distance carrier B is flat rate of $0.06 per minute. For a call that lasts t minutes, the cost of using carrier A is the same as the cost of using carrier B. If t is a positive integer greater than 20, what is the value of t?