simultaneous equations

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 =...

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)...

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...

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...

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...

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...

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...