68 Chapter 2 Linear Equations and Inequalities in One Variable Since 1900 checks in the equation, it is the solution and 2f + 300 = 2(1900) + 300 = 4100. So, Carrie invests $1900 in the first account and $4100 in the second account. 1e. Iron Man 2 ranks tenth in the list of all-time opening weeks at the box office. It earned approximately $36.1 million more than Iron Man in its opening week. Together, they earned $282.3 million in their opening weeks. How much did Iron Man and Iron Man 2 each earn in their opening weeks? (Source: http:// boxofficemojo.com/) Solution 1e. What is unknown? The opening week earnings of Iron Man and Iron Man 2 are unknown. Let x represent the earnings of Iron Man in millions of dollars. Then x + 36.1 represents the earnings of Iron Man 2 in millions of dollars. s 36.1 more than Iron Man What is given? Together, the two movies earned $282.3 million. Iron Man earnings + Iron Man 2 earnings is 282.3. x + x + 36.1 = 282.3 Express the relationship. 2x + 36.1 = 282.3 Combine like terms. 2x + 36.1 - 36.1 = 282.3 - 36.1 Subtract 36.1 from each side. 2x = 246.2 Simplify. 2x 246.2 = 2 2 Divide each side by 2. x = 123.1 Simplify. Since 123.1checks, it is the solution and x + 36.1 = 123.1 + 36.1 = 159.2. So, Iron Man earned $123.1 million and Iron Man 2 earned $159.2 million in their opening weeks. 1f. A DVD player now sells for $30. This is a 90% decrease in price from the original selling price of the DVD player. Find the original selling price of the DVD player. Solution 1f. What is unknown? The original selling price of the DVD player is unknown. Let x represent the original selling price. What is given? The DVD player now sells for $30. This is a 90% decrease from the original selling price, or 0.90x. We also know that the original selling price minus the decrease in price is the current selling price. original selling - decrease is current price in price selling price x - 0.90x = 30 0.10x = 30 0.10x = 0.10 30 0.10 Express the relationship. Combine like terms. Recall x - 0.90x = 1x - 0.90x = 0.10x. Divide each side by 0.10. x = 300 Simplify. Check: x - 0.90x =30 Begin with the original equation. 300 - 0.90(300) = 30 Replace x with 300. 300 - 270 = 30 Simplify. 30 = 30 True So, the original selling price of the DVD player was $300.
hendricks_intermediate_algebra_1e_ch1_3
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