Variables - ISEE Middle Level Quantitative Reasoning

If there are 3 students in each of Marie's art classes, and each student pays $15, this means that students are paying Marie $45 in total per class.

We can find the expense of the supplies by subtracting the amount Maria makes from the amount that the students pay her. The students pay her $45, but she only makes $35 per class.

The supplies must cost her $10.

Given that Joey's essay was 3 days late, he lost 15 points. This is because he loses 5 points for each day that it is late, and having turned it in 3 days late, lost 15 points.

Joey's final score (68) will be equal to his original grade, minus the penalty.

If we add 15 to the score that ultimately received, the sum is 83.

If Joey had turned his essay in on time, he would have earned a score of 83.

In solving for the first step is to substitute for , given that .

Next, the parentheses are solved for.

This simplifies to , the correct answer.

If Jack has a collection of 36 coins and gives Brett most of his collection, such that Brett now has twice as many coins as Jack, this problem can be solved by dividing the total into 3 equal parts, giving 2 of the parts to Brett and one of the parts to Jack

: this is Jack's part

: this is Brett's part

If Bob drove miles, and Anita drove twice as many miles as Bob, then Anita drove miles; therefore, the sum of the miles that they drove together would be 3J.

Thus, the correct answer is .

The first step is to translate the words, "if is added to of another number, the result is ," into an equation. This gives us:

Subtract from each side.

Multiply each side by .

Therefore, is the correct answer.

Multiply the constants and add an exponent to the variable totaling the number of variables in the equation:

Answer:

In modulo 13 arithmetic, a number is congruent to the remainder of the divison of that number by 13. Since

and

,

,

making the correct response 0.

In base five, each place value is a power of five, starting with 1 at the right, then, going to the left,

can be calculated in base ten as

.

In base five, each place value is a power of five, starting with 1 at the right, then, going to the left,

To convert a base ten number to base five, divide the number by the next lowest power of five, then divide each remainder by progressively lower powers.

Since , we start by dividing 387 by 125, and continue accordingly:

The base five equivalent of 387 is

By the order of operations, in the absence of grouping symbols, exponentiation (squaring here) takes precedence, followed by, in order, multiplication and addition.

By the order of operations, the operation within parentheses, which is addition, is carried out first; of the remaining two, multiplication precedes subtraction.

On Wednesday, Annie ran miles.

She ran more miles on Thursday than she did on Wednesday. Therefore, she ran miles on Thursday.

On Friday, she ran a distance in miles that was longer than the distance she ran on Wednesday. of miles is mile. (You can figure this out by realizing that since of is and is half of , of must be half of , which is .) , so Annie ran miles on Friday.

On Saturday, she ran a distance in miles that was longer than the distance she ran on Thursday. of is . , so Annie ran miles on Saturday.

The sum of these distances is equal to

Annie ran miles in total Wednesday through Saturday.

When adding and subtracting variable, you can only combine like variables.

That means all of the variables are solved separately from the variables.

Then you just add and subtract the constants normally so and .

So the final answer is .

When adding variables, it is true that you must first add all of the like variables. But then they are left separate to have an expression with the different variables differentiated.

Simplify by combining like terms.

We can begin by reordering our variables to have ones with the same exponent next to eachother.

Then, simply add the cofficients (numbers in front of the variables) of any variable with the same exponent

So our answer is:

When adding variables together, you must first make sure you are combining the same variable. So, in this case

we can see that both terms contain the variable a. Therefore, we can combine them.

Now, when we combine them, we can think of the variables as objects. So, we can say were are combining an apple and 4 apples together. So,

We can simplify our problem the same way.

Combine the following variables:

First, group the like terms. This means we will put terms with the same exponent next to each other. This will make it easier to be sure we are adding correctly.

Next, add the coefficients, but keep the exponents the same. Only combine terms with the same exponents. Notice that we have three different exponents (6,5 and 2) This means we will have three terms in our final answer.

So we get the following:

To add variables, we will think of the variables as objects. So, in the problem

let's think of the variable x as books. So, we can look at the problem as we currently have 3 books. We go to the library and borrow 7 more books. How many books do we have now? The answer is 10. We now have 10 books.

We can add the variables in the same way. So,

To add variables, we will look at the variables as objects. So,

we can look at it as the following. We have 6 dollars. We do all of our chores, and we get 4 more dollars. How many dollars do we have now? We now have 10 dollars. We add variables in the same way. So