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Math Help - System of Equations Involving Speed

  1. #1
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    Post System of Equations Involving Speed

    Hi people got a few math questions here that I need help with. (Okay some of them may seem ridiculously simple but I need the algebraic approach for all of them...)

    1. Mr A, Mr B and Mr C took part in a bicycle race. Mr A finished 12 minutes earlier than Mr B. Mr B finished 3 minutes before Mr C. If Mr A was 5 km/h faster than Mr B, and Mr B was 1/km/h faster than Mr C, find the distance of their race.

    2. A red ballpoint pen costs 19 cents, and a blue ballpoint pen costs 11 cents. Now that I pay a total of $2.80 for 16 pens, how many are blue pens?

    3. Clerk A takes 6 hours to type a report and clerk B takes 10 hours to type the same report. If clerk A starts to type for a few hours and then hands over the rest of the typing to clerk B, it will take 7 hours in total to complete. Find the number of hours each takes to type this report.

    4. Two iron ores, the first ores contain 68% of iron and the second ores contains 63% of iron ores. Now that 100 tonnes of 65% of iron ores are required, how much of each ores is to be used?

    5. Delivery order took a fleet of trucks over a number of days to fill. If 6 fewer trucks were used, then it would extend 3 days to complete the order. If 4 additional trucks were used, then it would take one less day to complete the order. Find the number of days and the number of trucks in this fleet.

    6. There were 360 door gifts for Founder's Day to be assembled over the weekend. Team A produced 112% of its quota; team B produced 110% of its quota. As a result, there were 400 door gifts assembled in total. Find the number of gifts in excess of the quota from each team.

    7. 30 English books and 24 Math books cost $83.40 in total. An English book costs 44 cents more than a Math book. Find the cost of the English book.

    8. A chemical of 80% concentration is to be mixed with the same chemical of 90% concentration to produce a 84% concentration chemical. For a 500 litres of this mixed chemical, find the amount used by each chemical.

    9. Alcohol of 72% concentration (A) is mixed with alcohol of 58% concentration (B) to make a mixture of 62% concentration. If 15 litres more of each alcohol are added to this mixture, the concentration becomes 63.25%. Find the amount of alcohol (litres) in A and B.

    Answering to ONE question is also okay! Thanks!
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  2. #2
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    System of equations

    Quote Originally Posted by chianyingxuan View Post
    Hi people got a few math questions here that I need help with. (Okay some of them may seem ridiculously simple but I need the algebraic approach for all of them...)

    1. Mr A, Mr B and Mr C took part in a bicycle race. Mr A finished 12 minutes earlier than Mr B. Mr B finished 3 minutes before Mr C. If Mr A was 5 km/h faster than Mr B, and Mr B was 1/km/h faster than Mr C, find the distance of their race.

    2. A red ballpoint pen costs 19 cents, and a blue ballpoint pen costs 11 cents. Now that I pay a total of $2.80 for 16 pens, how many are blue pens?

    3. Clerk A takes 6 hours to type a report and clerk B takes 10 hours to type the same report. If clerk A starts to type for a few hours and then hands over the rest of the typing to clerk B, it will take 7 hours in total to complete. Find the number of hours each takes to type this report.

    4. Two iron ores, the first ores contain 68% of iron and the second ores contains 63% of iron ores. Now that 100 tonnes of 65% of iron ores are required, how much of each ores is to be used?

    5. Delivery order took a fleet of trucks over a number of days to fill. If 6 fewer trucks were used, then it would extend 3 days to complete the order. If 4 additional trucks were used, then it would take one less day to complete the order. Find the number of days and the number of trucks in this fleet.

    6. There were 360 door gifts for Founder's Day to be assembled over the weekend. Team A produced 112% of its quota; team B produced 110% of its quota. As a result, there were 400 door gifts assembled in total. Find the number of gifts in excess of the quota from each team.

    7. 30 English books and 24 Math books cost $83.40 in total. An English book costs 44 cents more than a Math book. Find the cost of the English book.

    8. A chemical of 80% concentration is to be mixed with the same chemical of 90% concentration to produce a 84% concentration chemical. For a 500 litres of this mixed chemical, find the amount used by each chemical.

    9. Alcohol of 72% concentration (A) is mixed with alcohol of 58% concentration (B) to make a mixture of 62% concentration. If 15 litres more of each alcohol are added to this mixture, the concentration becomes 63.25%. Find the amount of alcohol (litres) in A and B.

    Answering to ONE question is also okay! Thanks!
    2 let x= number of red pens and 16-x blue pens.Write equation for cost of each set in terms of x= to 2.80



    4 let x= tons of 63% required and 100-x tons of 68%. As in 2 write equation so that total iron = 65 tons
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  3. #3
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    Quote Originally Posted by chianyingxuan View Post
    Hi people got a few math questions here that I need help with. (Okay some of them may seem ridiculously simple but I need the algebraic approach for all of them...)

    1. Mr A, Mr B and Mr C took part in a bicycle race. Mr A finished 12 minutes earlier than Mr B. Mr B finished 3 minutes before Mr C. If Mr A was 5 km/h faster than Mr B, and Mr B was 1/km/h faster than Mr C, find the distance of their race.



    Answering to ONE question is also okay! Thanks!
    1)Mr C time=t, speed=v
    B's time=t-3, speed=v+1 (1)
    A's time=(t-3)-12, speed=(v+1)+5 (2)
    Distance=speed/time, distance is same, equate 1 and 2
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  4. #4
    Member u2_wa's Avatar
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    I think you should first try it yourself and ask those questions of which you don't understand!!
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  5. #5
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    Quote Originally Posted by chianyingxuan View Post
    ...

    7. 30 English books and 24 Math books cost $83.40 in total. An English book costs 44 cents more than a Math book. Find the cost of the English book.

    ...
    1. Let p denote the price of an English book.

    2. Then you know:

    30p + 24(p-0.44)=83.4

    Solve for p.
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  6. #6
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    system of equations

    Quote Originally Posted by bjhopper View Post
    2 let x= number of red pens and 16-x blue pens.Write equation for cost of each set in terms of x= to 2.80



    4 let x= tons of 63% required and 100-x tons of 68%. As in 2 write equation so that total iron = 65 tons
    9 Solve for the ratio of A to B to make a 62% solution.Then write an equation in x=liters of B using the ratio as acoeff of x for liters of A.The equation will be an alcohol balance in one unknown
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