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Math Help - Word problems

  1. #1
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    Word problems

    Can you please explain how these problems are figured out? This is all the information I was given for each problem. I will be extremely grateful! Thank you!

    1. If the ratio of 2x to 5y is 3 to 4, what is the ration of x to y?

    2. Pat invested a total of $3000. Part of the money yields 10 percent interest per year, and the rest yields 8 percent interest per year. If the total yearly interest from this investment is $256, how much did Pat invest at 10 percent and how much at 8 percent?

    3. Two cars started from the same point and traveled ona straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles pere hour faster than the other car, what was the average speed for each car for the 2 hour trip?

    4. A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12. What is the cost per person if 40 people charter the aircraft?
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  2. #2
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    Quote Originally Posted by alaskamath View Post
    Can you please explain how these problems are figured out? This is all the information I was given for each problem. I will be extremely grateful! Thank you!

    1. If the ratio of 2x to 5y is 3 to 4, what is the ration of x to y?
    \dfrac{2x}{5y}=\dfrac34~\implies~\dfrac25 \cdot \dfrac xy=\dfrac34~\implies~\dfrac xy=\dfrac34 \cdot \dfrac52=\dfrac{15}8

    4. A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12. What is the cost per person if 40 people charter the aircraft?
    Let C denote the costs for the airplane. Then you know:

    \dfrac C{36}=\dfrac C{40}+12

    Solve for C.
    Spoiler:
    For information only:
    Spoiler:
    C = $4320.00
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  3. #3
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    Quote Originally Posted by alaskamath View Post
    Can you please explain how these problems are figured out? This is all the information I was given for each problem. I will be extremely grateful! Thank you!

    1. If the ratio of 2x to 5y is 3 to 4, what is the ration of x to y?

    2. Pat invested a total of $3000. Part of the money yields 10 percent interest per year, and the rest yields 8 percent interest per year. If the total yearly interest from this investment is $256, how much did Pat invest at 10 percent and how much at 8 percent?

    (1) 2x : 5y = 3 : 4

    2x/5y=3/4

    2/5(x/y)=3/4

    x/y=15/8

    (2) x yield 10% interest , (3000-x) yield 8% interest

     \frac{x}{10}+\frac{(3000-x) \cdot 8}{100}=256<br />

    solve for x . Then find the investment at 10 and 8 percent respectively .
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  4. #4
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    Talking

    Quote Originally Posted by alaskamath View Post
    3. Two cars started from the same point and traveled ona straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles pere hour faster than the other car, what was the average speed for each car for the 2 hour trip?
    To learn, in general, how to set up and solve the above sort of exercise, try here.

    Once you have studied the above....

    Note that they are moving in opposite directions, so their distances add together to get the total. Since the one car is defined in terms of the other, then:

    i) Pick a variable to stand for the rate of "the other car".

    ii) Create an expression, in terms of the variable in (i), for the rate of the "one car".

    iii) Note the given time value, and plug this and the variable from (i) into the "distance" equation "d = rt" to create an expression for the distance of "the other car".

    iv) Note the given time value, and plug this and the expression from (ii) into the "distance" equation to create an expression for the distance of the "one car".

    v) Recalling that their distances are additive, add the expressions from (iii) and (iv). Simplify.

    vi) Set the expression from (v) equal to the given total distance.

    vii) Solve the resulting linear equation for the value of the variable.

    viii) Use the definitions in (i) and (ii) to interpret your answer to (vii).

    If you get stuck, please reply showing your work and reasoning so far. Thank you!
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  5. #5
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    Quote Originally Posted by stapel View Post
    To learn, in general, how to set up and solve the above sort of exercise, try here.

    Once you have studied the above....

    Note that they are moving in opposite directions, so their distances add together to get the total. Since the one car is defined in terms of the other, then:

    i) Pick a variable to stand for the rate of "the other car".

    ii) Create an expression, in terms of the variable in (i), for the rate of the "one car".

    iii) Note the given time value, and plug this and the variable from (i) into the "distance" equation "d = rt" to create an expression for the distance of "the other car".

    iv) Note the given time value, and plug this and the expression from (ii) into the "distance" equation to create an expression for the distance of the "one car".

    v) Recalling that their distances are additive, add the expressions from (iii) and (iv). Simplify.

    vi) Set the expression from (v) equal to the given total distance.

    vii) Solve the resulting linear equation for the value of the variable.

    viii) Use the definitions in (i) and (ii) to interpret your answer to (vii).

    If you get stuck, please reply showing your work and reasoning so far. Thank you!

    I tried the websites and they were great!!! It helped me understand a lot more about speed and distance problems. Thanks.
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