SOLUTION: 1. Three CDs and 2 dvds cost �43 . 2 CDs and 3 DVD�s cost �47 . What is the cost of 1 cd I have some 20p pieces. I have twice as many pieces as 20p pieces . I have twice as m

Question 1119437: 1. Three CDs and 2 dvds cost �43 . 2 CDs and 3 DVD�s cost �47 . What is the cost of 1 cd
I have some 20p pieces. I have twice as many pieces as 20p pieces . I have twice as many 5p pieces as I have 10p pieces . I have �4.80 altogether. How many coins do I have ?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

first problem....

I will let other tutors provide a standard algebraic solution if they want; this problem allows a solution using logical reasoning and a bit of mental arithmetic.

3 CDs and 2 DVDs cost �43; 2 CDs and 3 DVDs cost �47. So "exchanging" one CD for one DVD increases the cost by �4.

So continue doing similar exchanges. 1 CD and 4 DVDs will cost �51; 0 CDs and 5 DVDs will cost �55.

Now we know the cost of each DVD is �11; substituting that value into any of the scenarios gives �7 as the cost of each CD.

second problem....

I will assume the missing part of the statement of the problem says you have twice as many 10p pieces as 20p pieces....

Then a simple way to solve this problem without formal algebra is to make groups of coins. From the given information, for each 20p piece you have two 20p pieces, and for each two 20p pieces you have four 5p pieces.

So make a group of one 20p piece, two 10p pieces, and four 5p pieces; the total value of that group is 20p+20p+20p = 60p. The number of those groups you need to make a total of �4.80 = 480p is 480/60 = 8.

And 8 groups of those coins means 8 20p pieces, 16 10p pieces, and 32 5p pieces.

Check: 8(20)+16(10)+32(5) = 160+160+160 = 480
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x, price of CD
y, price of of DVD

--------one additional equation to use. Use in the form of ; and use in the form of .
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