Paper Clips

Box A contained 579 paper clips. Box B contained 756 paper clips. After Kevin moved some paper clips from Box B to Box A, Box A contained twice as many paper clips as Box B.

b) How many paper clips did Kevin move from Box B to Box A?

Box A = 579 paper clips

Box B = 756 paper clips

Kevin moved some paper clips from Box B to Box A:

$\begin{array}{rcl} A+x &=& 2\cdot ( B-x ) \\ A+x &=& 2B-2x \\ 3x &=& 2B - A \\ x &=& \dfrac{2B-A}{3}\\ \hline \\ x &=& \dfrac{2\cdot 756- 579}{3} \\\\ x &=& \dfrac{933}{3} \\\\ x &=& 311 \\ \end{array}$

Kevin moved from Box B to Box A 311 paper clips

a) How many paper clips did Box B contain in the end?

$\begin{array}{rcl} B -x &=&756 - 311 = 445 \end{array}$

Box B did contain in the end 445 paper clips

Box A and Box B together contain 579 + 756 paper clips. So:

A + B = 579 + 756

A + B = 1335

Box A contains twice as many as Box B. So:

A = 2B

We can start by finding the B value through substitution:

A + B = 1335

Since A = 2B, we can replace A with 2B:

2B + B = 1335

And then combine like terms (2B+B):

3B = 1335

Now we can divide both sides by B to find:

B = 445

So the number of paper clips in Box B after the move is 445.

Now to find the number moved is simple; Subtract the new new B from the original B to find the difference:

Number moved = B₁ - B₂

Number moved = 756 - 445

Number moved = 311

I hopes that helps. That's what I consider a thorough answer for an algebra problem.

Box A contained 579 paper clips. Box B contained 756 paper clips. After Kevin moved some paper clips from Box B to Box A, Box A contained twice as many paper clips as Box B.

a) How many paper clips did Box B contain in the end?

b) How many paper clips did Kevin move from Box B to Box A?

579 + 756=1,335 total paper clips

1,335 / 3 =445 number of paper clips in Box B

445 X 2 =890 number of paper clips in Box A

756 - 445=311 number of paper clips that were moved from Box B to Box A

Box A contained 579 paper clips. Box B contained 756 paper clips. After Kevin moved some paper clips from Box B to Box A, Box A contained twice as many paper clips as Box B.

a) How many paper clips did Box B contain in the end?

b) How many paper clips did Kevin move from Box B to Box A?

579 + 756=1,335 total paper clips

1,335 / 3 =445 number of paper clips in Box B

445 X 2 =890 number of paper clips in Box A

756 - 445=311 number of paper clips that were moved from Box B to Box A