Simultaneous Equations Worded Examples

Transcription

1 Simultaneous Equations Worded Examples STUDENTS MUST STATE THE MEANING OF EACH VARIABLE 1. Two friends, Vicky and Richard, are each thinking of a number. Twice Vicky s number plus three times Richard s number is 43. The difference between their numbers is 4. Use simultaneous equations to find the value of the friends numbers. 2. Use simultaneous equations to find m and c: Using : 3. A son is 30cm shorter than his father. If the father is 1m taller, he would be twice his son s height. How tall is the father? 4. Each year a school has a concert of readings and songs. In 1999 the concert had 3 readings and 9 songs. It lasted 120 minutes. In 2000 the concert had 5 readings and 5 songs. It lasted 90 minutes. In 2001 the school plans to have 5 readings and 7 songs. Use simultaneous equations to estimate how long the concert will last. Call the time estimated for a reading minutes, and the time estimated for a song minutes. You must show your working.

2 Worded Simultaneous Equations 1. The sum of two numbers, and, is 140. If is 34 greater than, write down two equations in and. Solve them to find the two numbers. 2. If three ties and four shirts cost $241 and four ties and three shirts cost $200, find the cost of one tie and one shirt. 3. Winnie weighed some fruit on scales. She found that four mangoes and seven oranges weighed 450 grams, and 6 mangoes and 5 oranges weighed 510 grams. Using suitable letters, write down two simultaneous equations. Solve these equations and hence find the total weight of ten mangoes and four oranges. 4. The relationship between two variables, and, is given by the equation. If when and when, write down two simultaneous equations. Solve these equations to find and. 5. Mr. Knight bought five sheep and six goats for $183. From the same market Mrs Langton bought ten sheep and three goats for $204. What was the market charging for a sheep and a goat? 6. In an examination, candidates score marks for a correct answer and lose marks for an incorrect answer. Moses got 15 questions correct, 4 incorrect and scored 63 marks. Joseph got 12 questions correct, 7 incorrect and scored 39 marks. Find and. How many marks would Sarah score if she got 16 questions correct and 3 incorrect? 7. In a general knowledge contest, 3 marks are given for a correct answer and 1 mark is deducted for an incorrect answer. Ali answered 50 questions and scored 98. How many did he get right? 8. Ian has a pile of 40 coins, which are either 20 cents or 50 cents. The total value is 1490cents. How many does he have of each value?

3 Worded Simultaneous Equations Example: In my pocket I have 8 coins. They are $1 and $2 coins, and their total value is $11. How many of each type of coin do I have? number of $1 coins number of $2 coins 1. My friend has 12 coins in her pocket. They are all either 1 or 2. If the total value of her coins is 17, how many of each type does she have? 2. Two numbers have a sum of 45 and a difference of 13. Find the numbers. 3. When shopping in Jamaica, 5 coconuts and 14 bananas cost me $8.70, and 8 coconuts and 9 bananas cost $9.90. Find the cost of each coconut and each banana. 4. In my pocket I have only 5-cent and 10-cent coins. How many of each type of coin do I have if I have 24 coins altogether and their total value is $1.55? 5. The sum of two numbers is 49 and their difference is 19. Find the number. 6. The average of two numbers is 43 and their difference is 16. Find the numbers. 7. The average of two numbers is 20. If one of the numbers is doubled and the other is trebled, the average increases to 52. Find the number. 8. Four nectarines and three peaches cost 2.90, and three nectarines and a peach cost Find the cost of each fruit. 9. A visit to the cinemas costs 64 for a group of 2 adults and 5 children, and 68 for a group of 3 adults and 4 children. Find the cost of each adult ticket and each children s ticket. 10. Toby owns a fleet of trucks, and the trucks come in two sizes. The small trucks can carry a maximum of 3 tonnes, while the large trucks can carry a maximum of 5 tonnes. There are 25 trucks in Toby s fleet, and the trucks can carry a combined total of 95 tonnes. How many trucks of each size does Toby own? 11. Martin collects 20-cent and 50-cent coins. He has 37 coins, and the total value of the coins is $ How many coins of each type does Martin have? 12. A tailor made costumes for students to in a school play. Each male costume took 2 hours and cost $40 to make. Each female costume took 3 hours and cost $80 to make. In total the tailor spent 30 hours and $680 on the costume. How many male costumes and how many female costumes did the tailor make?

4 13. cm cm (x y) cm For the parallelogram alongside, find and. ( x y) cm 14. Ron the painter charges an hourly fee, as well as a fixed call-out fee, for his work. He charges $165 for a 2 hour job, and $345 for a 5 hour job. Find Ron s call-out fee and hourly rate. 15. Eric and Jordan were each given $8 to spend at a candy store. Eric bought 2 chocolate bars and 5 lolly bags, while Jordan bought 4 chocolate bars and 2 lolly bags. Neither child had any money left over. Find the cost of a chocolate bar.

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