simultaneous equations | Page 10 | MathCelebrity Forum

simultaneous equations

1. A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged \$4 per CD and \$6 per video and the total sales were \$180. Determine the total number of CDs and videos sold Let c be the number of CDs sold, and v be...
2. James is four time as old as peter if their combined age is 30 how old is James.

James is four time as old as peter if their combined age is 30 how old is James. Let j be Jame's age. Let p be Peter's age. We're given: j = 4p j + p = 30 Substitute (1) into (2) 4p + p = 30 Combine like terms: 5p = 30 Type 5p = 30 into our search engine, and we get p = 6. Plug p = 6 into...
3. 2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers

2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers. Let the first number be x, and the second number be y. We're given two equations: 2x - 4y = 6 x + y = 8 Using our simultaneous equation calculator, there are 3 ways to solve this: Substitution...
4. A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their pre

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their present ages? Let b be the boy's age and s be his sister's age. We're given two equations: b = s + 6 b + 3 = 2(s + 3) Plug in (1) to (2): (s + 6) + 3 = 2(s + 3) s + 9 = 2s + 6 Plugging this...
5. There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are i

There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are in the class? Let b be the number of boys and g be the number of girls. We are given 2 equations: g = b - 7 b + g = 33 Substitute (1) into (2): b + (b - 7) = 33 Combine like terms: 2b - 7 = 33...
6. Susan works as a tutor for \$14 an hour and as a waitress for \$13 an hour. This month, she worked a c

Susan works as a tutor for \$14 an hour and as a waitress for \$13 an hour. This month, she worked a combined total of 104 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month. Let t...
7. Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they? Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given: k = 0.5m k = l - 3 k + l + m = 39 Rearranging (1) by multiplying each side by 2, we have: m = 2k...
8. Two numbers that total 44 and have a difference of 6

Two numbers that total 44 and have a difference of 6. Let the two numbers be x and y. We're given the following equations: x + y = 44 <-- Total means a sum x - y = 6 Add the two equations together: (x + x) + (y - y) = 44 + 6 Cancelling the y terms, we have: 2x = 50 Typing this equation into...
9. A test has twenty questions worth 100 points total. the test consists of true/false questions worth

A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test? Let m be the number of multiple choice questions and t be the number of true/false...
10. One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a c

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers. Let the first number be x and the second number be y. We're given: x = 1/4y x + y = 25 Substitute (1) into (2) 1/4y + y = 25 Since 1/4 = 0.25, we have: 0.25y + y...
11. A first number plus twice a second number is 11. Twice the first number plus the second totals 34. F

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. Find the numbers. Let the first number be x and the second number be y. We're given: x + 2y = 11 2x + y = 34 Using our simultaneous equations calculator, we have 3 methods to solve this...
12. A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is \$37. The total cost to rent 2 chairs and 6 tables is \$64. What is the cost to rent each chair and each table? Let c be the cost of renting one chair and t be the cost of renting one table...
13. A Bouquet of lillies and tulips has 12 flowers. Lillies cost \$3 each, and tulips cost \$2 each. The b

A Bouquet of lillies and tulips has 12 flowers. Lillies cost \$3 each, and tulips cost \$2 each. The bouquet costs \$32. Write and solve a system of linear equations to find the number of lillies and tulips in the bouquet. Let l be the number of lillies and t be the number of tulips. We're given 2...
14. Ben is 3 times as old as Daniel and is also 4 years older than Daniel.

Ben is 3 times as old as Daniel and is also 4 years older than Daniel. Let Ben's age be b, let Daniel's age by d. We're given: b = 3d b = d + 4 Substitute (1) into (2) 3d = d + 4 Type this equation into our search engine, and we get d = 2. Substitute this into equation (1), and we get: b =...
15. The value of all the quarters and dimes in a parking meter is \$18. There are twice as many quarters

The value of all the quarters and dimes in a parking meter is \$18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter? Let q be the number of quarters. Let d be the number of dimes. We're given: q = 2d 0.10d + 0.25q = 18 Substitute (1) into (2)...
16. A cash register contains \$5 bills and \$20 bills with a total value of \$180 . If there are 15 bills t

A cash register contains \$5 bills and \$20 bills with a total value of \$180 . If there are 15 bills total, then how many of each does the register contain? Let f be the number of \$5 dollar bills and t be the number of \$20 bills. We're given the following equations: f + t = 15 5f + 20t = 180...
17. There were 175 tickets sold for the upcoming event in the gym. If students tickets cost \$5 and adult

There were 175 tickets sold for the upcoming event in the gym. If students tickets cost \$5 and adult tickets are \$8, tell me how many tickets were sold if gate receipts totaled \$1028? Let s be the number of student tickets and a be the number of adult tickets. We are given: a + s = 175 8a + 5s...
18. Kevin is 4 times old as Daniel and is also 6 years older than Daniel

Kevin is 4 times old as Daniel and is also 6 years older than Daniel. Let k be Kevin's age and d be Daniel's age. We have 2 equations: k = 4d k = d + 6 Plug (1) into (2): 4d = d + 6 Subtract d from each side: 4d - d = d - d + 6 Cancel the d terms on the right side and simplify: 3d = 6...
19. Alexis is working at her schools bake sale. Each mini cherry pie sells for \$4 and each mini peach pi

Alexis is working at her schools bake sale. Each mini cherry pie sells for \$4 and each mini peach pie sells for \$3. Alexis sells 25 pies and collects \$84. How many pies of each kind does she sell? Let each cherry pie be c and each peach pie be p. We have the following equations: c + p = 25 4c...
20. One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers. Let the two numbers be x and y. We're given: x = 1/5y x + y = 18 Substitute (1) into (2): 1/5y + y = 18 1/5 = 0.2, so we have: 1.2y = 18 Type 1.2y = 18 into the search engine, and we get y = 15...