Lesson Five - Distributive Property
Sale Prices
Used Games $9.95
Bargain Games $14.95
Regular Games $24.95
New Releases $34.95
Instant Replay Video Games sells new and used games. During a Saturday morning sale, the first "x" customers each bought a bargain game and a new release. Write an expression to calculate the total sales for these customers.
14.95x + 34.95x or (14.95 + 34.95)x = 49.90x
Instant Replay Video Games sells new and used games. During a Saturday morning sale, the first 8 customers each bought a bargain game and a new release. What will be the total sales to these customers? ($399.20)
Problem 1
The Morris family owns two cars. They drove the first car 18,000 miles and the second car 16,000 miles. Write an expression (using the distributive property) to calculate the cost to operate their cars in any year. Let x stand for the cost per mile to operate a car. Suppose that it is the same for the two cars.
18,000x + 16,000x = (18,000 + 16,000)x = 34,000x
Use the table to answer: The Morris family owns two cars. In 1998, they drove the first car 18,000 miles and the second car 16,000 miles. What will it cost the Morris family to operate their cars.
Car costs race ahead Prices (USA Today)
1985 .23
1990 .33
1995 .41
1998 .46
.46(18,000 + 16,000) = 15,640
Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.
1) twice the sum of s and t decreased by s.
2(s + t) -s
=2s + 2t - s (distributive rule)
=2s -s +2t (commutative rule)
= (2 - 1) s + 2t (distributive rule/combine like terms)
=s + 2t
2) five times the product of two and x increased by 3x
5(2x) + 3x (associative rule for multiplication)
=10x + 3x (combine like terms)
=13x (simplify)
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