Evaluating and Simplifying Expressions - PSAT Math

We are told that x&y = (x – y)xy .

–1&2 = (–1 – 2)(–1)(2) = (–3)–2

To simplify this, we can make use of the property of exponents which states that a– b = 1/(ab ).

(–3)–2 = 1/(–3)2 = 1/9

The answer is 1/9.

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.

You set up the equation to solve for a.

75 = 3000/(2(15) + a)

a = 10

You then set up the formula again for each movie costing $20, s(20)= 3000/(2(20) + 10), and solve for x, the number sold, giving you 60.

The "is" in the question means "equal," so whatever comes before "is" must be equal to whatever comes after. We will find an expression for the information before "is" and an expression for the information after "is," and then we will set these two expressions equal.

Twenty percent of a number can be represented as 0.2n, because 20% expressed as a decimal is 0.2, and because twenty percent "of" a number means the product of that number and twenty percent.

Four greater than the product of a number and six means that we must first find the product of that number and six, and then increase this value by 4.

The product of a number and six means that we must multiply this number by six, which can be represented by 6n. Increasing 6n by 4 can be modeled by the expression 6n + 4, or 4 + 6n (because of the commutative property of addition).

Setting the two expressions equal gives us 0.2n = 4 + 6n .

There are B+G total students in the elementary school class, so G out of B+G are girls.

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.

The easiest way to solve this problem is to guess-and-check the answer choices. The equation that can be used to match the table will be correct.

We can see that the values in the table match the equation for each given value. Thus, this must be our answer.

We can also determine certain characteristics from the table itself. For example, as x increases, y(x) decreases. This tells us that there is likely a negative coefficient, which can help narrow down the answer options.

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.

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.

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.

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.

To evaluate an expression we make substitutions into the expression

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

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

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.

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.

First, we need to evaluate 5&3.

Since x&y = xy – x + y, we can find 5&3 as follows:

5&3 = 5(3) – 5 + 3

= 15 – 5 + 3

= 13

Now, we need to go through each of the choices and determine which one equals 13.

Let's start with 2&(8&1). Remember that we must first evaluate inside the parantheses.

2&(8&1) = 2&(8(1) – 8 + 1)

= 2&(8 – 8 + 1)

= 2&(1)

= 2(1) – 2 + 1 = 1, which doesn't equal 13.

Next, let's evaluate 4&(3&4).

4&(3&4) = 4&(3(4) – 3 + 4)

= 4&(13) = 4(13) – 4 + 13 = 61.

Next, we can evaulate 8&(2&0).

8&(2&0) = 8&(2(0) – 2 + 0)

= 8&(–2) = 8(–2) – 8 + 2 = –22.

Next, let's find 3&(5&2).

3&(5&2) = 3&(5(2) – 5 + 2)

= 3&(7) = 3(7) – 3 + 7 = 25.

Finally, lets evaluate 11&(0&2).

11&(0&2) = 11&(0(2) – 0 + 2)

= 11&(2) = 11(2) – 11 + 2 = 13.

The answer is 11&(0&2).

Just take this step by step. First write out each equation:

x = 0.75y

y = 8(1.5z)

First, simplify the second equation:

y = 12z

Then, substitute y from this equation into the first:

x = 0.75(12z) = 9z

The key to solving this question is noticing that we can factor out a two:

2x + 6y = 44 is the same as 2(x + 3y) = 44

Therefore, x + 3y = 22

In this case, x + 3y + 33 is the same as 22 + 33 or 55

Let's make 3 equations based on our data:

J = 4S + 4

P = 3J

S = 20

All we have to do is sequentially replace values.

Substitute 20 for S in the J equation:

J = 4 * 20 + 4 = 84

Now, we can calculate P: P = 3 * 84 = 252