How to add variables

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ISEE Upper Level Quantitative Reasoning › How to add variables

Questions 1 - 10
1

Add:

Explanation

In order to simplify this expression, we will need to add like terms.

There is a lone positive three.

Combine all the terms.

The answer is:

2

Simplify:

Explanation

3

Multiply:

Explanation

4

Simplify:

Explanation

Combine like terms:

5

If two supplementary angles are equal to and , then what is the value of ?

Explanation

The sum of two supplementary angles is always 180 degrees; therefore:

6

Simplify:

Explanation

First we rewrite the problem so that like terms are together.

Next we can place like terms in parentheses and evaluate the parentheses.

Now we rewrite the equation in simplest form.

7

On Gina's swim team, 40 percent of the swimmers also play one other sport (cross country, soccer, or baseball) competitively. There are 20 people on her swim team. Of the swimmers who play one other sport, 2 of them participate in cross country, and twice as many people play soccer as those who play baseball. How many play soccer?

Explanation

On Gina's swim team, 40 percent of the swimmers also play one other sport competitively. Given that there are 20 people on her swim team, 8 people play one other sport because 40 percent of 20 is 8.

If 2 swimmers run cross country that leaves 6 swimmers who play a different sport.

Given that twice as many play soccer as those who play baseball, it follows that 4 play soccer and 2 play baseball.

Thus, 4 is the correct answer.

8

Simplify:

Explanation

First, rewrite the problem so that like terms are next to each other.

Next, evaluate the terms in parentheses.

Rewrite the expression in simplest form.

9

Simplify the following:

Explanation

Simplify the following:

To combine the given expression, we need to realize that we can only combine terms with the same exponent.

In this case, all our terms have the same exponents, so we can add them up just like we would any integer.

To add up our terms, simply add up the coefficients and keep the exponent the same. (With this in mind we could eliminate any answer choices which do not have an exponent of two)

So, do the following:

\

So, we have our answer of 60 x squared

10

Combine the following:

Explanation

When adding variables, we will look at the variables like objects.

So, in the problem

we can think of the variable b as books. So,

We can read it like this: We borrowed 3 books from the library yesterday. We go back to the library and borrow 5 more books. How many books have we borrowed altogether? We have borrowed 8 books. So,

We add variables the same way.

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