elimination

There are 812 students in a school. There are 36 more girls than boys. How many girls are there? Let b be boys Let g be girls We're given two equations: b + g = 812 g = b + 36 Rearrange equation 2 to subtract b from each side: b + g = 812 -b + g = 36 Add equation (1) to equation (2): b...

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation Assumptions: Let m be the number of multiple choice questions Let s...

4 adults and 3 children cost $40. Two adults and 6 children cost $38 Givens and Assumptions: Let the number of adults be a Let the number of children be c Cost = Price * Quantity We're given 2 equations: 4a + 3c = 40 2a + 6c = 38 We can solve this system of equations 3 ways Substitution...

Alberto and Willie each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Alberto spent $64 on 3 daylilies and 8 pots of ivy. Willie spent $107 on 9 daylilies and 7 pots of ivy. What is the cost of one daylily and the cost of one pot of ivy...

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina? Assumptions and givens: Let Justin's age be j Let Martina's age be m j > m (since Justin is older than Martina) We're given the following equations : j - m = 22 j + m = 54...

the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 kids is $51. the bill for 3 adults and 1 kid is $45. what is the cost per adult and per kid? Let the cost for each adult be a Let the cost for each kid be k We're given two equations: 2a + 3k =...

A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the values of a and b. plug in both points and form 2 equations: 5a - 2b = 23 1x - 5b = 23 We can solve this simultaneous equations any one of three ways: Substitution Method Elimination Method...

2 pens and 1 eraser cost $35 and 3 pens and 4 erasers cost $65. X represents the cost of 1 pen and Y represents the cost of 1 eraser. Write the 2 simultaneous equations and solve. Set up our 2 equations where cost = price * quantity: 2x + y = 35 3x + 4y = 65 We can solve this one of three...

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slices of pie costs $20.20. what is the cost of one cupcake? Let the number of cupcakes be c Let the number of pie slices be p Total Cost = Unit cost * quantity So we're given two equations: 1c +...

Some History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of $750. Mr. Alexander spent $682, getting 28 student...

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the...

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel Let the number of cups of coffee be c Let the number of bagels be b. Since cost = Price * Quantity, we're...

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 the number of cd's be c and number of...

Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she works as a tutor and makes$12 per hour. One week she worked 30 hours and made$268 . How many hours did she spend at each job? Let the cashier hours be c. Let the tutor hours be t. We're...

The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00. Paul sold 15 ivy plants and 6 ferns for 240. What’s the selling price of each plant. Let the cost of each fern be f Let the cost of each ivy plant be I We're given: 12f + 8i = 260 15i + 6f =...

The first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drinks for $54. Find the cost for each pizza and each drink Assumptions: Let the cost of each pizza be p Let the cost of each drink be d Givens: 4d + 3p = 33.50 6d + 5p = 54 We have a...

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Assumptions: B = the speed of the boat in still water. S = the speed of the stream Relative to the...

In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & tricycles were in the bike shop? Let b be the number or bicycles and t be the number of tricycles. Since each bicycle has 2 wheels and 1 seat and each tricycle has 3 wheels and 1 seat, we have...

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations: a + c = 414...

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted? Let the number of children's tickets be c. Let the number...