SOLUTION: Hi Box A contains $1 coins box B contains 50 cent coins and box C contains 20cent coins. A has 5 times as many coins as C. B has 12 fewer than A. C has half the number in B. How

Question 1199590: Hi
Box A contains $1 coins box B contains 50 cent coins and box C contains 20cent coins. A has 5 times as many coins as C. B has 12 fewer than A. C has half the number in B. How much money is in box A.
Thanks
Found 3 solutions by math_tutor2020, greenestamps, josgarithmetic:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

A = number of coins in box A
B = number of coins in box B
C = number of coins in box C

Stated facts:

A has 5 times as many coins as C.
B has 12 fewer than A.
C has half the number in B
Let's translate each of those three statements into symbolic form.
A = 5C from fact 1
B = A-12 from fact 2
C = 0.5B from fact 3
Then apply a combination of fact 1 and fact 3.
A = 5C
A = 5*0.5B
A = 2.5B

Now involve fact 2 so we can solve for B.
B = A-12
B = 2.5B-12
B-2.5B = -12
-1.5B = -12
B = -12/(-1.5)
B = 8
There are 8 coins worth 50 cents each in box B.

Then,
A = 2.5B
A = 2.5*8
A = 20
There are 20 coins worth $1 each from box A.
Ultimately we have 20*1 = 20 dollars in box A.

Answer: $20

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

A has more coins than C; B has fewer than A; and C has half as many as B. Since the number in C is smallest....

Let x = # of coins in C
Then 2x = # of coins in B
And 5x = # of coins in A

The number of coins in B is 12 less than the number in A:

2x = 5x-12
3x = 12
x = 4

The number of coins in A is 5x = 5*4 = 20.

ANSWER: 20*($1) = $20

Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!

A, of $1, a
B of $0.5, b
C, of $0.10, c

-------substitute this into the part, .

------the substitution

-------------------makes for $20 .

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