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Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 socks did Ralph buy? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8

 Nov 8, 2019

Best Answer 

 #1
avatar+2391 
+2

Here is how u solve this (i solved this 2 days ago so the memory is fresh):

 

Set up equation - 

\(x+y+z=12\)        (total socks)

\(x+3y+4z=24\)   (total money)

 

X is $1 socks, Y is $3 socks, and Z is $4 socks.

 

 

Use elimination to rid of X. - 

\(2y+3z=12\)


Now guess and check the solutions for (y,z).

After guessing and checking, we find out that the only solution is (3,2).

 

So we substitute it back into our original equation \(x+y+z=12\)

 

And solve

\(x+3+2=12\)

\(x=7\)

 

 

Answer should be \(\boxed{\text{(D) }7}\)

.
 Nov 8, 2019
edited by CalculatorUser  Nov 8, 2019
 #1
avatar+2391 
+2
Best Answer

Here is how u solve this (i solved this 2 days ago so the memory is fresh):

 

Set up equation - 

\(x+y+z=12\)        (total socks)

\(x+3y+4z=24\)   (total money)

 

X is $1 socks, Y is $3 socks, and Z is $4 socks.

 

 

Use elimination to rid of X. - 

\(2y+3z=12\)


Now guess and check the solutions for (y,z).

After guessing and checking, we find out that the only solution is (3,2).

 

So we substitute it back into our original equation \(x+y+z=12\)

 

And solve

\(x+3+2=12\)

\(x=7\)

 

 

Answer should be \(\boxed{\text{(D) }7}\)

CalculatorUser Nov 8, 2019
edited by CalculatorUser  Nov 8, 2019
 #2
avatar+104933 
0

Nice work, CU!!!

 

 

 

cool cool cool

CPhill  Nov 8, 2019

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