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# Explain this AMC8 question for me plz!

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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 +2847 +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 $$\boxed{\text{(D) }7}$$

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Nov 8, 2019
edited by CalculatorUser  Nov 8, 2019

#1
+2847
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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
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Nice work, CU!!!

CPhill  Nov 8, 2019