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When trying to match an equation to a verbal description, it is usually easier to work backwards from the verbal descriptions. In other words, write the equation for each verbal description and match your equation to the given equation.

Let's say that you were given the equation 3x + 20 = y and you were told to match it to one of the verbal descriptions given below.

Description 1: The hypotenuse of a triangle is 20 more than the short leg and the long leg is 3 times as the long as the short leg. What is y, the perimeter of the triangle, if x is the length of the short leg?

Let's start translating Description 1 into algebraic language.

Let x = length of the short leg	This was given in the description.
Then 3x = length of the long leg	Also given in the description.
And x + 20 = length of the hypotenuse	Also given in the description.

To find y, the perimeter of the triangle, you need to add all the sides, so the equation would be

Short leg + long leg + hypotenuse = perimeter

x + (3x) + (x + 20) = y

4x + 20 = y This equation does NOT match the given equation 3x + 20 = y.

Description 2: The hypotenuse of a triangle is 15 more than the short leg. The long leg of the triangle is 5 more than the short leg. What is y, the perimeter of the triangle, if x is the length of the short leg?

If you translate Description 2 into algebraic language, you would write

Let x = length of the short leg	This was given in the description.
Then x + 5 = length of the long leg	Also given in the description.
And x + 15 = length of the hypotenuse	Also given in the description.

To find y, the perimeter of the triangle, you need to add all the sides, so the equation would be

Short leg + long leg + hypotenuse = perimeter

x + (x + 5) + (x + 15) = y

3x + 20 = y This equation DOES match the given equation 3x + 20 = y.

Now it's time for you to try a few. Use your notes to explain why or why not a given verbal description matches the given equation.

Equation	Verbal Description	Answer
1. y = x + 5	Maria has 5 times as many t-shirts as Julie. What is y, the total number of t-shirts that Maria has, if Julie has x t-shirts?	Check Your Answer The equation does NOT match the description. Since Maria has 5 times as many t-shirts, that would be written as 5x not x + 5. To find the total number of shirts between the two girls, add Maria's shirts to the number of Julie's t-shirts, giving the expression 6x.
2. y = 4x + 20	The length of a rectangle is 20 more than the width. What is y, the perimeter of the rectangle, with a width of x inches?	Check Your Answer This equation does NOT match the description. Since the perimeter would be found by adding 2 widths (2x) and 2 lengths [2(x + 20)] to find the perimeter.
3. y = 4x	What is y, the perimeter of a square, with a side length of x inches?	Check Your Answer This equation DOES match the description. Since you find the perimeter of a square by adding all the sides (x + x + x + x = 4x).
4. y = x + 3	Gary is 3 years older than his brother Joseph. What is y, the total of their ages, if Joseph is x years old?	Check Your Answer This equation does NOT match the description. Since you need to find the total of their ages, you would need to find the sum of Joseph's age (x) and Gary's age (x + 3). This would make the sum of their ages 2x + 3 instead of x + 3.
5. y = 48 + 8x	Callie is keeping a record of her new puppy’s weight. When she got the puppy, he weighed 48 ounces. If the puppy gains x ounces each week, what is y, his total weight, after 8 weeks?	Check Your Answer This equation DOES match the description. Since the puppy gains x ounces each week, his weight for 8 weeks would be represented by 8x and this would be added to his original weight of 48 ounces (8x + 48).