Algebraic Expressions Worksheets 4

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Algebraic Expressions Worksheets 4

In the previous set of worksheets, we had problems in which students had to write two variables in terms of a third one, and then combine this information into a single expression. For example:

Write the sum of John's, Henry's and Alicia's ages, if Henry is twice as old as John, and Alicia is three years older than John.

J = John's age
H = Henry's age = 2J
A = Alicia's age = J + 3

J + H + A = J + 2J + J + 3 = 4J + 3

In all of these problems, it was a simple matter to write an expression with one variable, since two of the quantities were given in terms of the third quantity. But that won't always be the case. Consider this problem, which is identical to the previous example, except for one word:

Write the sum of John's, Henry's and Alicia's ages, if Henry is twice as old as John, and Alicia is three years older than Henry.

J = John's age
H = Henry's age = 2J
A = Alicia's age = H + 3

In this case, we can't write the sum in terms of one variable, unless we do one more substitution:

A = Alicia's age = H + 3 = 2J + 3

Now we can write: J + H + A = J + 2J + 2J + 3 = 5J + 3

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Lesson by Mr. Twitchell

Handouts/Worksheets

Algebraic Expressions Worksheet #4.1

For each phrase below, pick variables to represent the unknowns. State what the variables represent, and then write the phrase as an algebraic expression in one variable.

Example: The longest side of a triangle is twice the length of the shortest;
the middle is 3 less than the length of the longest. Write the perimeter.
Solution: S = shortest side, L = longest side = 2S; M = middle side = L - 3 = 2S - 3;
S + M + L = S + 2S - 3 + 2S = 5S - 3

The perimeter of a triangle, if the shortest side's length is half the longest, and the middle side's length is two more than the shortest
The sum of three numbers, if the first is five more than the second, and the third is half the first
The sum of my test scores, if the first was five more than the second, and the third was twenty less than the first
The sum of two numbers, minus twice a third number, if the first number is two more than the second, and the third is 5 less than twice the first
The product of two numbers, plus a third number, if the second number is half of the third number, and the first number twice the second number
The difference between Sam's age and Jonas's age, if Sam is seven years older than Mark, and Mark is twice as old as Jonas
Half the difference between the first number and twice the second number, if the first number is two more than the third number, and the second number is two less than the third number
The area of a rectangle, if the width is two more than twice a number, and the length is 5 less than three times that number
The change received after purchasing 3 boxes of cereal and 2 blocks of cheese, if a block of cheese costs $3 more than a box of cereal, and the total amount of money used to pay is 10 times the cost of block of cheese
The sum of the ages of three boys, if the oldest boy is 20 years older than the youngest, and the middle boy is half the age of the oldest.

Algebraic Expressions Worksheet #4.1: Answer Key

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