# ISEE Middle Level Math : How to add variables

## Example Questions

### Example Question #161 : Variables

The sum of four consecutive numbers is 62. What is the smallest number?

Explanation:

The algebraic way to solve this problem is to set up an equation, however, students can also solve using guess-and-check from the answer options.

When setting up an equation, sequential numbers are equal to , and . We know the sum of these sequential numbers to be 62, allowing us to set up the following equation:

Combine like-terms by reordering.

Subtract 6 from each side of the equation, then divide each side by 4 in order to isolate the variable.

### Example Question #162 : Variables

Rewrite the base-ten number 387 in base five.

Explanation:

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

### Example Question #118 : Algebra

Maria teaches an art class. She makes $35 for each class she teaches, and art supplies are her only expense. How much must the supplies cost if each class is priced at$15 per student, and she always has 3 students in each class?

Explanation:

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.

### Example Question #2281 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Joey's teacher takes off 5 points from student essays each day the essay is late. The essays are scored out of 100 points. If Joey's essay got a score of 68, but he turned it in 3 days late, what would his score have been if he had turned the essay in on time?

Explanation:

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.

### Example Question #120 : Algebra

Write in base ten:

Explanation:

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

.

### Example Question #51 : Operations

Annie ran  miles on Wednesday. She ran  more miles on Thursday than she did on Wednesday. On Friday, she ran a distance in miles that was  longer than the distance she ran on Wednesday. On Saturday, she ran a distance in miles that was  longer than the distance she ran on Thursday. What is the total number of miles that Annie ran, Wednesday through Saturday?

Explanation:

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.

### Example Question #52 : Operations

Bob and Anita drove cross country together. If Bob drove  miles on the trip, and Anita drove twice as many miles as Bob, how many miles total did they drive together?

Explanation:

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.

### Example Question #1 : Expressions & Equations

If  is added to  of another number, the result is . What is the other number?

Explanation:

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

### Example Question #53 : Operations

Jack has a collection of coins. He gives Brett most of his collection, such that Brett now has twice as many coins as Jack. If there are 36 coins in the collection, how many coins does Jack now have?

Explanation:

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

### Example Question #54 : Operations

If , what is the value of ?