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Math Help - Ughhh another word problem...help

  1. #1
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    Ughhh another word problem...help

    Wow i just cant seem to get any of these word problems right. I just dont have a good formula, and i guess im having a hard time trying to figure out the question itself...although i know the question is not complicated i just cannot find a forumula or an answer!

    any help?

    Heres the Q's First one:
    A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of a solution that is 50% alcohol?

    Second:
    An electronics store put two types of car radios on sale. One model sold for $87, and the other sold for $119. During the sale, the receipts for the 25 radios sold were $2,495. How many of the less expensive radios were sold?

    stuff is so confusing to me...but i wanna master it, just need some help

    Thanx guys
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  2. #2
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    You can do it! Figure out your knowns and unknowns, and just find some way to relate them mathematically (it sounds like the latter step is where you're having difficulty). This should get you off the ground:

    Quote Originally Posted by Baginoman View Post
    Heres the Q's First one:
    A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of a solution that is 50% alcohol?
    What are our unknowns? We need to find the volume of the 40% solution needed (call it x), and the volume of the 55% solution that is needed (call it y). We know the total amount should come to 15 liters, so this gives us one equation:

    x + y = 15

    But we also know that the final solution should be 50% alcohol, so this gives us our second equation: Because there is 40\%\cdot x = 0.4x liters of alcohol in the x liters of the first solution, and 55\%\cdot y = 0.55y liters of alcohol in the y liters of the second solution, the final solution will have a total of 0.4x + 0.55y liters of alcohol, which should come to 50% of the total 15 liters:

    0.4x + 0.55y = 0.5\cdot15 = 7.5

    You now have two equations with two unknowns.

    Quote Originally Posted by Baginoman View Post
    Second:
    An electronics store put two types of car radios on sale. One model sold for $87, and the other sold for $119. During the sale, the receipts for the 25 radios sold were $2,495. How many of the less expensive radios were sold?
    Again, what are the unknowns? We have two types of radios, each selling a certain number of units (call the number of cheap radios x, and the number of the others y). We know that 25 radios were sold in total, so that gives

    x + y = 25

    but we also know that the total revenue brought in from the radios was $2495, which gives us

    87x + 119y = 2495

    Again, you will just need to solve this system of linear equations.
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  3. #3
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    thankyou so much, that helped alot!
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