# ISEE Upper Level Quantitative : How to find the solution to an equation

## Example Questions

### Example Question #61 : Algebraic Concepts

In an aquarium, the ratio of sharks to clown fish is . If there are  more clown fish than sharks, how many sharks are there?

Explanation:

Set up a proportion, where .

Cross multiply:

Distribute:

Combine like terms:

Divide both sides of the equation by 5:

There are 64 sharks.

### Example Question #62 : Algebraic Concepts

In June, a company had a profit of  million. In July, the company doubled that profit. In August, the company's profits rose by  percent. If profits rise by another  percent in September, what is the September profit?

million

million

million

million

million

million

Explanation:

The profit in July is twice the profit in June, or \$6 million.

Because profits rise by 15% in August, August's profit is really 115% of July's profit:

Similarly, September's profit is 115% of August's profit:

### Example Question #63 : Algebraic Concepts

Evaluate .

Explanation:

Subtract expressions:

or

### Example Question #64 : Algebraic Concepts

If  and , evaluate

It is impossible to tell from the information given.

Explanation:

Solve for

Explanation:

### Example Question #742 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which is the greater quantity?

(A)

(B)

(A) is greater

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

(A) is greater

Explanation:

This makes (A) greater.

### Example Question #743 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which of the following is the greater quantity?

(A)

(B)

(B) is greater

(A) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(A) and (B) are equal

Explanation:

The quantities are equal.

### Example Question #744 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

If , then what is ?

Explanation:

To solve this problem, simply plug the numbers into the equation: . Then, just simplify. This gives you , which is

### Example Question #745 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Column A                 Column B

The quantity in Column B is greater.

The quantity in Column A is greater.

The quantities in both columns are equal.

The realtionship between the columns cannnot be determined.

The quantities in both columns are equal.

Explanation:

and mean that you must plug in what it's inside the parantheses to x in the function. Therefore, when you plug in -2 to the function, you get , which is 11. Then, plug in 2 to the function, which gives you , which is also 11. Therefore, the columns are equal.

### Example Question #746 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Column A                              Column B

The slope of                           The slope of

the line                                  the line perpendicular

.                      to the line in Column A.

There can be do relationship determined.

The quantity in Column A is greater.

The quantities are equal.

The quantity in Column B is greater.