Pens are $9 per dozen and pencils are $6 per dozen. Janet needs to buy a half dozen of each for school. How much is the total cost of her purchase?
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Khan Academy Solving Equations with the Distributive Property
Guidance
Recall that the distributive property is a mathematical way of grouping terms. It states that the product of a number and a sum is equal to the sum of the individual products of the number and the addends. Here, you will use the distributive property with equations that contain decimals and/or fractions. The same rules apply. If the equation has parentheses, your first step is to multiply what is on the outside of the parentheses by what is on the inside of the parentheses. After you remove parentheses, you then solve the equation by combining like terms, moving constants to one side of the equals sign and variables to the other side of the equals sign, and finally isolating the variable to find the solution.
Example A
Solve: .
Solution:
Find the LCD for 5, 5, and 1. Since it is 5, multiply the last number by , to get the same denominator.
Since all of the denominators are the same, the equation becomes:
Therefore .
Example B
Solve: .
Solution:
Find the LCD for 4, 4, and 1. Since it is 4, multiply the last number by , to get the same denominator.
Since all of the denominators are the same, the equation becomes:
Therefore .
Example C
Solve: .
Solution:
Since all of the denominators are the same, the equation becomes:
Therefore .
Concept Problem Revisited
Pens are $9 per dozen and pencils are $6 per dozen. Janet needs to buy a half dozen of each for school. How much is the total cost of her purchase?
First you should write down what you know:
Let total cost
Cost of pens: $9/dozen
Cost of pencils: $6/dozen
Janet needs one half dozen of each.
The total cost would therefore be:
Therefore Janet would need $7.50 to buy these supplies.
Vocabulary
- Distributive Property
- The distributive property is a mathematical way of grouping terms. It states that the product of a number and a sum is equal to the sum of the individual products of the number and the addends. For example, in the expression: , the distributive property states that the product of a number and a sum is equal to the sum of the individual products of the number and the addends and .
Guided Practice
1. Solve for x: .
2. Solve for x: .
3. Solve for x: .
Answers:
1.
Find the LCD for 2, 2, and 1. Since it is 2, multiply the last number by , to get the same denominator.
Since all of the denominators are the same, the equation becomes:
Therefore .
2.
Find the LCD for 3, 3, and 1. Since it is 3, multiply the last number by , to get the same denominator.
Since all of the denominators are the same, the equation becomes:
Therefore .
3.
Find the LCD for 3, 3, and 4, 4. Since it is 12, multiply the first two fractions by and the second two fractions by , to get the same denominator.
Since all of the denominators are the same, the equation becomes:
Practice
Solve for the variable in each of the following equations.