CREATING EXPRESSIONS AND EQUATIONS FROM WORD PROBLEMS FOR SAT

Problem 1 :

On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?

A) 9mp        B) 20mp      C) 5 + 4 m p      D) 4 + 5 m p

Solution :

Number of text messages Armand sent = m

Number of hours it takes = 5

Number of messages from Armand = 5m

Number of text messages Tyrone sent = n

Number of hours it takes = 4

Number of messages from Tyrone = 4n

Total number of messages = 5m + 4n

Problem 2 :

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck’s revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?

A) 77         B) 93        C) 99          D) 105

Solution :

Cost of salads = $6.50

Cost of drink = $2

Number of salads be s and number drinks be d.

s + d = 209 ----(1)

Revenue :

6.50s + 2d = 836.50----(2)

(1) x 2 ==> (2s + 2d) - (6.50s + 2d) = 418 - 836.50

2s + 2d - 6.50s - 2d = 418 - 836.50

-4.50 s = -418.5

s = 418.5/4.50

s = 93

So, number of salads is 93.

Problem 3 :

An object travels at a constant speed of 12 centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel 108 centimeters?

A) 9       B) 96     C) 120    D) 972

Solution :

The object travels 12 centimeters in 1 second.

It should travel for 108 centimeters.

= 108/12

= 9

So, it will take 9 minutes.

Problem 4 :

At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

Solution :

Let x be the amount of calories in each fries.

Amount of calories in each hamburgers = x + 50

2 hamburgers + 3 fries = 1700 calories

2 (x + 50) + 3 x = 1700

2x + 100 + 3x = 1700

5x + 100 = 1700

5x = 1600

x = 1600/5

x = 340

Amount of calories in hamburgers = 340 + 50

= 390 calories

Problem 4 :

The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true?

A) 30 = 2 x      B) 2 = 30 x     C) x/2 = 30      D) x + 30 = 2

Solution :

30 states are joined the United States between 1776 and 1849.

Number of states joined in between 1850 and 1900 = x

The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900.

2(30) = x

30 = x/2

So, option C is correct.

Problem 5 :

The monthly membership fee for an online television and movie service is $9.80. The cost of viewing television shows online is included in the membership fee, but there is an additional fee of $1.50 to rent each movie online. For one month, Jill’s membership and movie rental fees were $12.80. How many movies did Jill rent online that month?

A) 1        B) 2      C) 3         D) 4

Solution :

Let x be the number of movies rented.

Service fee = $9.80

Additional fee for each movie = 1.50

Service charge + amount for renting movies = 12.80

1.50 x + 9.80 = 12.80

Subtracting 9.80,

1.50x = 12.80 - 9.80

1.50x = 3

x = 3/1.50

x = 2

On that month Jill rented 2 movies.

Problem 6 :

b = 2.35 + 0.25x

c = 1.75 + 0.40x

In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

A) $2.60       B) $2.85     C) $2.95      D) $3.35

Solution :

b = 2.35 + 0.25x -----(1)

c = 1.75 + 0.40x -----(2)

b = c

2.35 + 0.25x = 1.75 + 0.40x

0.25x - 0.40x = 1.75 - 2.35

-0.15x = -0.6

x = 0.6/0.15

x = 4

Applying the value of x in (1), we get

b = 2.35 + 0.25 (4)

b = 2.35 + 1

b = 3.35

Problem 7 :

If a 3-pound pizza is sliced in half and each half is sliced into thirds, what is the weight, in ounces, of each of the slices?

(1 pound = 16 ounces)

A) 4     B) 6       C) 8      D) 16

Solution :

3 pound pizza = 3/2 ==> 1.5 pounds of pizza

1.5 pound pizza is sliced into thirds = 1.5/3

= 0.5 pounds of pizza

1 pound = 16 ounces 

0.5 pounds = 0.5(16)

= 8 ounces

So, each slice will be 8 ounces.

Problem 8 :

The density of an object is equal to the mass of the object divided by the volume of the object. What is the volume, in milliliters, of an object with a mass of 24 grams and a density of 3 grams per milliliter?

A) 0.125       B) 8      C) 21     D) 72

Solution :

Let D be the density, M be mass of the object and V be the volume.

D = M/V

Mass = 24 grams, density = 3

3 = 24/V

V = 24/3

V = 8 grams

So, the volume is 8 grams.