PROBLEMS ON RATES FOR SAT

Problem 1 :

A faulty register records only $5 for every $8 deposit. If the register shows a total balance of $40, what is the actual balance ?

(a)  $25    (b) $64    (c)  $80     (d)  120

Solution :

For every $8, it registers only $5.

For x dollars deposit, it will show $40.

8 : 5 = x : 40

8 / 5 = x / 40

x = 8(40) / 5

x = 64

So, the actual balance should be $64.

Problem 2 :

During a trip, Jonathan had driven a total of 75 miles by 6:20 PM and a total of 85 miles by 6:40 PM. He drove at the same rate for the entire trip. At what time has he driven a total of 140 miles ?

(a)  7:30 PM    (b) 8:00 PM    (c)  8:30 PM     (d)  9:00 PM

Solution :

Difference between two timings = 20 minutes

For every 20 minutes, Jonathan is covering 10 miles.

20 minutes : 10 miles = x minutes : 65 miles

20/10 = x/65

2(65) = x

x = 130 minutes

x = 2 hours 10 minutes 

6:20 ->7:20->8:20 + 10 minutes

So, the answer is 8:30 PM

Problem 3 :

A train is travelling at an average speed of 80 miles per hour takes 8 hours to complete a given trip. How much time would it take the train to complete the same trip if it traveled at an average speed of 120 miles per hour ?

(a)  4 hours    (b) 4 hours 30 minutes

(c)  5 hours 20 minutes     (d)  5 hours 30 minutes

Solution :

Average speed = 80 miles per hour

Distance covered in 8 hours = 80(8)

= 640 miles

The distance given above should be covered with the average speed of 120 miles per hour.

Time taken = 640/120

= 5.3 hours

= 5 hours 20 minutes

Problem 4 :

At a certain pizza restaurant 8 ounces of cheese is enough for 2/3 of a pizza. Given that there are 16 ounces in pound, how many pizzas can be produced with 12 pounds of cheese ?

Solution :

1 pound = 16 ounces 

12 pounds = 12 x 16

= 192 ounces

8 ounces is enough to make 2/3 of pizza.

Number of pizzas can be made with 192 ounces

= (192/8) x (2/3)

= 16 pizzas.

Problem 5 :

At a movie theater, an adult ticket costs $10 and a bag of popcorn costs $6. If a group of adults bought tickets to a movie and 4 bags of popcorn, what expression could be used to determine how much in total the group spent in dollars ?

(a) 10x + 6, where x is the total number of adults.

(b) 10x + 24, where x is the total number of adults.

(c)  16x, where x is the total number of adults.

(d)  6x+10, where x is the total number of popcorn purchased.

Solution :

Let x be the number of adults. $10 be cost of 1 ticket.

10x = the cost spending for tickets.

Number of popcorns they are purchasing = 4

Cost of 1 bag of popcorn = $6

Amount spent for popcorn = 6(4) => 24

So, the required cost will be 10x + 24

Problem 6 :

On Friday, Jaince read x pages every 30 minutes for 4 hours and Kim read y pages every 15 minutes for 5 hours. Which of the following represents the total number of pages read by Jaince and Kim on Friday ?

(a)  4x + 5y     (b)  8x + 20y    (c)  20x + 8y    (d)  120x + 75y

Solution :

About Jaince :

Number of 30 minutes in 1 hour = 2

in 4 hours = 8 (30 minutes).

Number of pages read by Jaince = 8x

About Kim :

Number of 15 minutes in 1 hour = 4

in 5 hours = 20 (15 minutes).

Number of pages read by Kim = 20y

So, total number of pages = 8x + 20y

Problem 7 :

A salad dressing supplier ensures that there are 7.5 ounces of salad dressing in every container. How many containers would be required to hold 150 ounces of salad dressing?

Solution :

Every container will have 7.5 ounces of salad.

Number of container = 150/7.5

= 20 containers

Problem 8 :

A small shop can manufacture 4 windows every 5 hours. At the rate, how long will it take to manufacture 7 windows ?

(a) 8 hours                  (b)  8 hr 15 minutes

(c) 8 hr 30 minutes     (d)  8 hr 45 minutes

Solution :

5 hours = 4 windows 

Let x be the number of hours.

5 : 4 = x : 7

(5/4) = (x/7)

x = 35/4

x = 8.75

8 hours 45 minutes

Problem 9 :

A car has gas mileage of 32 miles per gallon when it travels at an average speed of 65 miles per hour. If the car travels for t hours at 65 miles per hour, which of the following expressions represents the amount of gas, in gallons, the car consumed ?

(a)  32/65t       (b) 65/32t       (c)  32t/65        (d)  65t/32

Solution :

Using 1 gallon of gas, the car covers the distance of 32 miles.

Speed of the car = 65 miles per hour

Time taken = t hours

Distance should be covered = 65t miles

For every 1 gallon of gas, it can cover 32 miles.

Amount of gas required = 65t/32

Problem 10 :

A textbook company ships its books in boxes that can hold 30 pounds. One particular order calls for shipment of 800 books. If each book weights 1.4 kilograms, how many boxes will be required to fulfills this order ? (1 kilograms = 2.2 pounds)

Solution :

Weight of 1 book = 1.4 kilograms

number of books = 800

weight of 800 books = 800 (1.4)

= 1120 kilograms

Converting kilograms to pounds :

= 1120 (2.2)

= 2464 pounds

1 box can hold = 30 pounds

Required number of boxes = 2464/30 ==> 82.13

So, we need 83 boxes.

Problem 11 :

A technology company finds that 11 out of every 600 emails sent through its servers are lost. At this rate, how many emails are lost if 42000 emails are sent through its servers ?

Solution :

600 mails = 11 are lossing

1 mail = 11/600

42000 mails = (11/600) x 42000 

= 770 lost

Problem 12 :

Kevin has collected m coins. Ellie has collected half as many as Kevin, but 5 more than Robert. In terms of m, how many coins has Robert collected ?

(a) 2m - 5     (b)  (m/2) + 5    (c)  2m + 5     (d)  (m/2) - 5

Solution :

Number of coins collected by Kevin = m

If x is the number of coins collected by Robert.

Ellie has collected = x - 5

m/2 = x - 5

x = (m/2) + 5

Problem 13 :

Jane receives $2.75 each month for each square foot of an apartment that she rents out. If the apartment has an area of 500 square feet, how much rent, in dollars would Jane receive from a tenant who occupies the entire area for one year ?

(a)  16500     (b)  17250    (c)  18375      (d)  19750

Solution :

The amount receives by Jane for 1 square foot = $2.75

Total area = 500

Amount he receives in total = 500(2.75)

= 1375 for a month.

Since, he occupies the area for a year,

required amount = 12 x 1375 

= 16500

Problem 14 :

Mary runs around a circular track with a radius of 25 meters. If she runs at 75 meters per minute, how many minutes will it take to run one lap around the track, rounded to the nearest integer ?

Solution :

Radius of the circular track = 25 meters

Circumference of the circle = 2 πr

= 2 x 3.14 x 25

= 157 meters 

Running rate = 75 meters

To cover 157 meters, she needs = 157/75

= 2.09 

So, the answer is 2 minutes.

Problem 15 :

A movie rental service charges $15 as a monthly subscription fee and $3 per movie rented. If Alex rents x movies per month from this service, which of the following gives the total amount, in dollars, he spends on movie rentals in one year ?

(a)  12x    (b)   15 + 12(3x)    (c)  12(15) + 3x    (d) 12(15 + 3x)

Solution :

x be the number of movies he rented.

Monthly subscription = $15

Per year subscription = 12(15)

Rent per move = 3

Amount spent for rent = 3x

Total amount = 12(15) + 3x