Dividing 56 into Two Parts

Yeva

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Apr 27, 2009
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My mom and I have been puzzling over this for some time. Even the "Teacher's Key" didn't have any way of working it out.

Divide 56 into two parts such that 3 eighths of the larger number decreased by 6 equals 1 fourth of the smaller number.

Helping would be very appreciated.
 
Yeva said:
My mom and I have been puzzling over this for some time. Even the "Teacher's Key" didn't have any way of working it out.

Divide 56 into two parts such that 3 eighths of the larger number decreased by 6 equals 1 fourth of the smaller number.

Helping would be very appreciated.

Start with naming variables - what needs to be found.

Let the larger number = L

smaller number = S = 56 - L .............................................(1)

3 eighths of the larger number decreased by 6

3/8 * L - 6


1 fourth of the smaller number

1/4 * (56 - L)


Now what .......
 
Yeva said:
Divide 56 into two parts such that 3 eighths of the larger number decreased by 6 equals 1 fourth of the smaller number.
Seems to work only if changed to:
Divide 56 into two parts such that 3 eighths of (the SMALLER number decreased by 6)
equals 1 fourth of the LARGER number.

In other words: 3/8(S - 6) = L/4

Et tu, Subhotosh ?
 
Denis said:
Yeva said:
Divide 56 into two parts such that 3 eighths of the larger number decreased by 6 equals 1 fourth of the smaller number.
Seems to work only if changed to:
Divide 56 into two parts such that 3 eighths of (the SMALLER number decreased by 6)
equals 1 fourth of the LARGER number.

You flipped smaller and larger in the problem......

In other words: 3/8(S - 6) = L/4

Et tu, Subhotosh ? <<< Sir Denis ...You hurt me....
 
Subhotosh Khan said:
Denis said:
Yeva said:
Divide 56 into two parts such that 3 eighths of the larger number decreased by 6 equals 1 fourth of the smaller number.
Seems to work only if changed to:
Divide 56 into two parts such that 3 eighths of (the SMALLER number decreased by 6)
equals 1 fourth of the LARGER number.

You flipped smaller and larger in the problem......

In other words: 3/8(S - 6) = L/4

Et tu, Subhotosh ? <<< Sir Denis ...You hurt me....

Fixing that - that is your flipped interpretation of smaller and larger - your interpretation will give

3/8(L-6) = 1/4(56 - L)

and get

L = 26 and S = 30 <<< But that cannot be by definition - so my interpretation is correct


that (3 eighths of the larger number )decreased by 6 equals 1 fourth of the smaller number.

- that is the correct equation to solve is:

3/8*L - 6 = 1/4 * (56 - L)
 
WHOA! I'm saying a solution is possible ONLY if the problem is worded this way:

Divide 56 into two parts such that 3 eighths of (the SMALLER number decreased by 6)
equals 1 fourth of the LARGER number.
Thus: 3/8(S - 6) = L/4 : brackets REQUIRED!
 
Denis said:
… I'm saying a solution is possible ONLY if the problem is [reworded] …

… (3/8)(S - 6) = L/4 : brackets REQUIRED!


The given information does not contain parentheses; therefore, the phrase "3 eighths of the larger number decreased by 6" means (3/8)L - 6. This is how Subhotosh set up the system.

Did you try to solve it, Denis?

3/8ths of 32 is 12, and 12 decreased by 6 is 6.

1/4th of 24 is 6.

6 = 6 : kapish? :twisted:

(BTW, "Shakespeare Day" was last week; it's over, now.)

 


Is this compelling evidence that watching hockey rots your mind? :wink:

 
Re:

mmm4444bot said:


Is this compelling evidence that watching hockey rots your mind? :wink:

Evidently so...particularly if your team is losing :roll:
 
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