Grade 12 Math: Creating Equations from Word Problems
This worksheet focuses on translating advanced word problems into algebraic equations, covering various mathematical concepts for Grade 12 students.
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Grade 12 Math: Creating Equations from Word Problems
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Read each word problem carefully and translate it into a mathematical equation. Do not solve the equations unless specified.
1. A rectangular garden has a perimeter of 80 meters. If the length of the garden is 10 meters more than its width, write an equation to represent the perimeter in terms of the width (w).
2. Sarah invested $5000 in two different accounts. One account pays 4% annual interest and the other pays 6% annual interest. If she earned a total of $260 in interest after one year, write an equation to represent the amount invested in the 4% account (x).
3. The product of two consecutive positive integers is 156. Let the first integer be 'n'. The equation representing this situation is .
4. A box has a volume of 216 cubic centimeters. Its length is twice its width, and its height is 3 cm less than its width. If 'w' represents the width, the equation for the volume is .
5. The time it takes to travel a certain distance is inversely proportional to the speed. If it takes 3 hours to travel 180 miles at a certain speed, which equation represents the relationship between time (t) and speed (s) for the same distance?
t = 180s
t = s/180
t = 180/s
s = 180t
6. The speed of a boat in still water is 15 mph. It travels 30 miles upstream and 30 miles downstream in a total of 4 hours. If 'c' is the speed of the current, which equation represents this situation?
30/(15+c) + 30/(15-c) = 4
30/(15-c) - 30/(15+c) = 4
15c + 15c = 4
30(15+c) + 30(15-c) = 4
7. A theater sold 500 tickets for a play. Adult tickets cost $15 and student tickets cost $10. If the total revenue from ticket sales was $6500, write a system of two equations to represent the number of adult tickets (a) and student tickets (s) sold.
8. A chemist needs to mix a 20% acid solution with a 50% acid solution to produce 100 ml of a 30% acid solution. Let 'x' be the volume of the 20% solution and 'y' be the volume of the 50% solution. Write a system of two equations to represent this situation.