WRITE ALGEBRAIC EXPRESSIONS FOR THE FOLLOWING PRACTICE 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) 5m + 4p       D) 4m + 5p

Solution:

Armand sent m text messages each hour for 5 hours.

Total messages sent by Armand = 5m

Tyrone sent p text messages each hour for 4 hours

Total messages sent by Tyrone = 4p

Total messages sent by both = 5m + 4p

So, option (C) is correct.

Problem 2 :

If 16 + 4x is 10 more than 14, what is the value of 8x?

A) 2     B) 6     C) 16     D) 80     

Solution:

We have, 

16 + 4x = 14 + 10 

4x = 24 - 16

4x = 8

x = 2

So, 8 × 2 = 16

So, option (C) is correct.

Problem 3 :

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:

Let s be the number of salads sold.

Then number of drinks sold = 209 − s

Since the earning was 836.50, we have

6.5s + 2(209 − s) = 836.5

6.5s + 418 − 2s = 836.5

4.5s = 418.5

s = 93

Thus, 93 salads were sold.

So, option (B) is correct.

Problem 4 :

Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?

Solution:

Let the laptop's original cost be = L

After 20 % discount its price will be (100 − 20)% × L = 0.8L

8 % sales tax on this price = (100 + 8)% × 0.8L = 1.08 × 0.8L

So, p = 1.08 × 0.8L

So, option (D) is correct.

Problem 5 :

Katarina is a botanist studying the production of pears by two types of pear trees. She notices that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina's observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?

A) 115         B) 120            C) 124           D) 173

Solution:

Since Katarina notices that Type A trees produced 20 percent more pears than Type B trees did therefore,

Since Type A trees produced 144 pears, the "20 percent more" than the same amount is 120% that is:

Hence, if the Type A trees produced 144 pears, then Type B trees produced 120 pears.

So, option (B) is correct.

Problem 6 :

Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?

Solution:

Wyatt can husk anywhere from  12 to  18 dozen ears of corn per hour.

Thus, if we need to find the time taken to husk 72 dozen ears of corn.

The maximum time would be 72/12 ​= 6 hours

 The minimum time would be 72/18 ​= 4 hours

Thus, depending on his speed, Wyatt takes anywhere from 4 to 6 hours to husk 72 dozen ears of corn.

Problem 7 :

The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge's posted weight limit?

Solution:

Total weight of the truck = 14x + 4500

It should be < 6000 pounds

14x + 4500 < 6000

14x < 1500

x < 107.15

Thus there should be maximum 107 boxes.

Problem 8 :

A partially filled pool contains 600 gallons of water. A hose is turned on, and water flows into the pool at the rate of 8 gallons per minute. How many gallons of water will be in the pool after 70 minutes?

Solution:

In 70 minutes, gallons of water flowing into the pool

= 70 × 8 = 560

So total water = 600 + 560 = 1160 gallons

Problem 9 :

If x is the average (arithmetic mean) of m and 9,y is the average of 2m and 15 and z is the average of 3m and 18, what is the average of x, y and z in terms of m ?

A) m + 6       B) m + 7       C) 2m + 14      D) 3m + 21

Solution:

Given,

So, option (B) is correct.