substitution

the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers Let the first small number be x. Let the second larger number be y. We're given: x + y = 5 5y + 4x = 37 We can solve this 3 ways, using the following methods: Substitution Method...

Twice a first number decreased by a second number is 16. The first number increased by 3 times the second number is 1. Find the numbers. Let the first number be x and the second number be y. We're given: 2x - y = 16 x + 3y = 1 Using our simultaneous equations calculator, you can solve this 3...

The team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score? Let a be the amount of points A scored, and b be the amount of points B scored. We're given: a = b + 13 a + b = 47 Plug (1) into (2) (b + 13) + b = 47 Combine like terms: 2b + 13...

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...

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...

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...

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...

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers Let the first number be a and the second number be b. We have: a + 2b = 7 2a + b = 23 Rearrange (1) into (3) (3) a = 7 - 2b Substitute (3) into (2): 2(7 - 2b) + b = 23 Multiply...

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $90 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $33,000. How many shares of each stock does he own? Set up the given equations, where A...

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage Let d be Devaughn's age. Let s be Sydney's age. We have two equations: d = 2s d + s = 78 Substitute (1) into (2) 2s + s = 78 3s = 78 Entering 3x = 78 into the search engine, we get s = 26.

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which system of linear equations represents the given situation? Let a be the number of the $13 book, and b equal the number of $17 books. We have the following system of linear equations: a + b = 88...

If a+b=16, then what is 3a+3b= Factor 3a + 3b: 3(a + b) Since we know a+b = 16, we have: 3(16) = 48

Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. How many pairs does Jenny have and how many pairs does her brother have? Let j be the number of shoes Jenny has and b be the number of s hoes her brother has. Set up 2 equations: (1) b + j = 25 (2)...

If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have? Let h = Mr. Hernandez's students and d = Mr. Daniels students. We are given two equations: (1) h = 5d (2) d + h = 150 Substitute equation (1) into equation (2) d +...

Let g = Gary's pets and a = Abe's pets. We are given two equations: (1) g = a - 3 (2) a + g = 15 Substitute (1) into (2) a + (a - 3) = 15 Combine Like Terms: 2a - 3 = 15 Add 3 to each side: 2a = 18 Divide each side by 2 to isolate a: a = 9 --> Abe has 9 pets Substitute a = 9 into Equation...

Michelle and Julie sold 65 cupcakes. If Julie sold 9 more cupcakes than Michelle, how many cupcakes did each of them sell? Let m = Michelle's cupcakes and j = Julie's cupcakes. We have two equations: m + j = 65 j = m + 9 Substituting, we get: m + (m + 9) = 65 Combine like terms, we get: 2m...