Mix Questions - Worksheet 1

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Chapter 3 Class 10 Linear Equations In Two Variables - Mix Questions Worksheet 1 by teachoo Chapter: Chapter 3 Class 10 Maths – Linear Equations in Two Variables Name: _____________________________ School: _____________________________ Roll Number: _____________________________ 1. (2 Marks) A nutritionist is mixing two types of juices. Juice A has 10 mg of Vitamin C per 100 ml , and Juice B has 20 mg of Vitamin C per 100 ml . The final mixture of 500 ml must have exactly 80 mg of Vitamin C. Formulate a pair of linear equations to find the amount of each juice required. (Do not solve). 2. (2 Marks) Two friends are saving money. Anjali starts with ₹100 and saves ₹20 per week. Ben starts with ₹0 and saves ₹30 per week. The equations are A=20w+100 and B=30w. Explain what the solution to this system represents in the context of their savings. 3. (2 Marks) The paths of two asteroids are given by the equations x-2y=3 and 2x-4y=5. An astronomer claims they will collide. Is she correct? Justify your answer using the concept of consistency of equations, without drawing a graph. 4. (2 Marks) A rectangle's length is three times its width. If the perimeter is 80 cm , find the dimensions. Model this with equations and find the length and width. 5. (2 Marks) A taxi service charges a fixed fee plus a per-kilometer charge. A 10 km journey costs ₹150, and a 15 km journey costs ₹220. What do the variables in your equations represent? Find the fixed fee. 6. ( 2 Marks) Look at the graph below. It shows the cost of two different pizza places based on the number of toppings. Which pizza place is cheaper if you want exactly 3 toppings? Explain how you found the answer from the graph. (A simple graph would be drawn with two intersecting lines. Line A starts at y=10 and has a gentle slope. Line B starts at y=8 and has a steeper slope. They intersect at (2,14)). 7. (2 Marks) The sum of two numbers is 50. One number is 10 more than the other. When you represent this with equations, what does the ordered pair ( x,y ) of the solution stand for? 8. ( 3 Marks) A chemistry student needs to make a 100 ml solution that is 25% acid. She has two stock solutions: one is 10% acid and the other is 30% acid. Set up the system of linear equations to find out how much of each stock solution she should mix. Solve for the required volumes. 9. (3 Marks) A digital artist is creating a design using two types of geometric shapes: triangles (t) and squares (s). Each triangle takes 2 minutes to draw and each square takes 3 minutes. She wants to draw exactly 15 shapes and has a total of 40 minutes. a) Formulate the equations. b) Solve the system to find out how many of each shape she can draw. 10. (3 Marks) The population of Town A is decreasing linearly, modeled by P_A=50000-500t. The population of Town B is increasing linearly, modeled by P_B=35000+250t, where t is the number of years from now. a) In how many years will their populations be equal? b) What will be the population of each town at that time? Important links Answer of this worksheet - https://www.teachoo.com/25590/5361/Mix-Questions---Worksheet-1/category/Teachoo-Questions---Mix/ Full Chapter with Explanation, Activity, Worksheets and more – https://www.teachoo.com/subjects/cbse-maths/class-10th/ch3-10th-pair-of-linear-equations-in-two-variables/ Science Class 10– https://www.teachoo.com/subjects/science/class-10/ Maths Class 10- https://www.teachoo.com/subjects/cbse-maths/class-10th/ For more worksheets, ad-free videos and Sample Papers – subscribe to Teachoo Black here - https://www.teachoo.com/black/ Answer Key to Mix Questions Worksheet 1 Let x be the volume of Juice A and y be the volume of Juice B. Equations: x+y=500 and 0.10x+0.20y=80. The solution represents the number of weeks (w) after which Anjali and Ben will have the same amount of money. No. For the lines to be parallel, a_1/a_2 =b_1/b_2 ≠c_1/c_2 . Here, 1/2=(-2)/(-4) but 1/2≠3/5. The paths are parallel and will never intersect (collide). Equations: l=3w and 2(l+w)=80. Solution: Width =10" " cm, Length =30" " cm. Let f be the fixed fee and c be the charge per km. The fixed fee is ₹ 10 . Place B is cheaper. At x=3, the line for Place B is below the line for Place A, indicating a lower cost. The ordered pair (x,y) represents the two numbers themselves. Let x be the volume of 10% solution and y be the volume of 30% solution. Equations: x+y=100 and 0.10x+0.30y=25. Solution: 25 ml of 30% solution and 75 ml of 10% solution. a) t+s=15,2t+3s=40. b) 5 triangles, 10 squares. a) In 20 years. b) The population of both towns will be 40,000 .