SAT Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #1 : How To Evaluate Algebraic Expressions

A total of 150 million votes were tallied in a presidential election. Votes were cast for either Hillary Clinton, Rand Paul, Al Gore, or Gary Johnson. If Clinton received 3 times the number of votes as Johnson, Paul received 30% of the vote, and Gore receieved 30 million total votes, who received the most votes in the election?

Possible Answers:

Gary Johnson

Rand Paul

Al Gore

Hillary Clinton

Correct answer:

Hillary Clinton

Explanation:

There are a few ways to do this problem, but we will focus on the total number of votes method as follows. First, let Clinton = C, Gore = G, Paul = P, and Johnson = J. We know C + G + P + J = 150 million. We also know that C = 3J. Paul received 30% of the vote which is 150,000,000 * .3 = 45 million votes. Gore received 30 million votes. We can now create an equation with individual totals and substitute 3J for Clinton's vote total:

3J + 30 million + 45 million + J = 150 million

4J = 75 million

J = 18.75 million

Then C = 3J = 56.25 million. So Clinton received 56.25 million votes, Paul received 45 million votes, Gore received 30 million votes, and Johnson received 18.75 million votes.  The correct answer is Hillary Clinton.

Example Question #2 : Evaluating Expressions

Justin makes 61.9% of his free throws. During the season he had 84 free throw attempts.  How many of Jason’s shots did not go in?

Possible Answers:

52

32

40

36

21

Correct answer:

32

Explanation:

Find how many free throws Justin made:  84 x 0.619 = 51.99.  Since the problem talks free throws, we round to 52 shots went in.  To calculate shots missed:

84 – 52 = 32.

Example Question #2 : Evaluating And Simplifying Expressions

If 5x + 30 = 6 – 7x, then x = ?

Possible Answers:

x = 2

x = –18

x = –37

x = –10

x = –2

Correct answer:

x = –2

Explanation:

Combine like terms by subtracting 6 from both sides so:  5x + 24 = –7x.  Then subtract 5x from both sides:  24 = –12x.  Divide both sides by –12 and x = –2.

Example Question #4 : Evaluating Expressions

If ab - bc + d = d2 - c2, then what is the value of a when b is two, c is negative one, and d is zero?

 

 

Possible Answers:
3/2
-1
-3/2
-1/2
1/2
Correct answer: -3/2
Explanation:

ab - bc + d = d2 - c2

We need to substitute values in for b, c, and d, and then solve the equation for a.

a(2) - 2(-1) + 0 = 02 - (-1)2

2a +2 + 0 = 0 - (1)

2a + 2 = -1

2a = -3

a = -3/2

The answer is -3/2.

Example Question #3 : Evaluating And Simplifying Expressions

If 11x + 4 = 19x – 12, then what is 2x – 4?

Possible Answers:

2

4

Not possible

0

–8

Correct answer:

0

Explanation:

First solve for x. The first equation would simplify as:

16 = 8x

x = 2

If we plug x = 2 into the second expression:

2(2) – 4 = 0 

0 is the correct answer.

Example Question #4 : Evaluating And Simplifying Expressions

If x = 2 and y = 3, then evaluate 2(x – 3) + 5y2

Possible Answers:

37

43

62

49

52

Correct answer:

43

Explanation:

To evaluate an expression we make substitutions into the expression

2(x – 3) + 5y2 becomes 2(2 – 3) + 5 * 32 = –2 + 45 = 43

Example Question #3 : Evaluating And Simplifying Expressions

IF 5x3 = 40, then what is the value of 12x – (x/2)?

Possible Answers:

10

17

33

24

23

Correct answer:

23

Explanation:

Use the first equation to solve for x, then plug into the 2nd equation to find a value.

5x3 = 40

x3 = 8

x = 2

12(2) – (2/2) = 24 – 1 = 23

Example Question #4 : Evaluating And Simplifying Expressions

A rowing team paddles upstream at a rate of 10 miles every 2 hours and downstream at a rate of 27 miles every 3 hours. Assuming they are paddling at the same rate up and downstream, what is the speed of the water?

Possible Answers:

2

5

7

Cannot be determined

1

Correct answer:

2

Explanation:

Upstream:        p – w = (10/2)    or     p – w = 5 miles/hour

Downstream:    p + w = (27/3)    or    p + w = 9 miles/hour

Then we add the two equations together to cancel out the w's. After adding we see

2p = 14

p = 7 miles/hour   where p is the rate of the paddling. We plug p into the equation to find

w = 2 miles/hour    where w is the rate of the stream's water.

Example Question #5 : Evaluating And Simplifying Expressions

Tim is two years older than his twin sisters, Rachel and Claire. The sum of their ages is 65. How old is Tim?

Possible Answers:

22

24

20

23

21

Correct answer:

23

Explanation:

The answer is 23. 

Since Rachel and Claire are twins they are the same age. We will use the variable r to represent both Rachel and Claire's ages. 

From the question we can form two equations. They are:

t = r + 2       and     65 = t + 2r

lets plug the first equation into the second to solve for r.

65 = (r + 2) + 2r

65 = 3r +2

63 = 3r

r = 21      This means Rachel and Claire are 21 years old. Plug this into the equation so

t = 23       Tim is 23 years old. 

Example Question #1 : Evaluating Expressions

Drink A is 20% water by weight, and drink B is 35% water by weight. How many fluid ounces of drink A must be added to 80 oz of drink B to have a drink whose final proportion of water is 30%?

Possible Answers:

40 fl oz

60 fl oz

85 fl oz

75 fl oz

50 fl oz

Correct answer:

40 fl oz

Explanation:

It's easiest if we convert all percentages to actual oz of water for each step here. As such, 35% of the 80 oz of drink B would have 0.35(80) = 28 oz of water in it. 

We can set up an equation that similarly converts each "percentage of a fixed weight of liquid" to ensure that our final weight is equivalent to 30% to the sum of drink A and B. On the left side, the fixed values are the percentages of each drink individually, and on the right side is what the question requires as a fixed percentage of the final weight:

0.2(A) + 0.35(80) = 0.3(A + 80)

0.2A + 28 = 0.3A + 24

A = 40 

Solving for A, we get 40 oz of A that must be poured into B. You may plug this back into the equation to check it.

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