Translating Word Problems into Equations

A notebook costs $3 more than a pen. Maya bought 4 pens and 2 notebooks for $24. Define the unknown and find the cost of one pen.

Let x be the price of a pen in dollars. Notebook is x + 3. Equation: 4x + 2(x + 3) = 24. 6x + 6 = 24, giving 6x = 18. A pen costs $3.

Danny is 6 years older than Yossi. In 4 years, the sum of their ages will be 40. How old is Yossi today?

Let x be Yossi's current age. Danny is x + 6. In 4 years: (x + 4) + (x + 10) = 40. 2x + 14 = 40, so 2x = 26. Yossi is 13 years old today.

A jacket was discounted by 20%. The sale price is $64. What was the original price?

Let x be the original price in dollars. Equation: 0.8x = 64. Divide by 0.8 to get x = 80. The original price was $80.

A rectangle has an area of 60 square meters. Its length is 7 meters longer than its width. Find its width and explain any rejected values.

Let x be the width. Length is x + 7. Equation: x(x + 7) = 60, so x^2 + 7x - 60 = 0. Factoring gives (x - 5)(x + 12) = 0. Solutions are 5 and -12. Reject -12 because width cannot be negative. The width is 5 meters.

An item's price rose by 20%, then fell by 25%. The final price was 90 dollars. Find the original price.

Let x be the original price. After rise: 1.2x. After fall: 1.2x * 0.75 = 0.9x. Equation: 0.9x = 90. The original price was 100 dollars.