Question

Giovanni has 2,080 green, red, and yellow Legos in his collection. He has three times as many green Legos as red Legos. He has twice the number of yellow Legos as green Legos. If he trades of his yellow legos for an equal number of 1/3 red Legos, how many red Legos will he have in total?

Answer 1

Let the number of red Legos be \( r \). According to the problem:

- The number of green Legos is \( 3r \).
- The number of yellow Legos is \( 2 \times (3r) = 6r \).

Now, we can express the total number of Legos in terms of \( r \):

\[
r + 3r + 6r = 2,080
\]

This simplifies to:

\[
10r = 2,080
\]

Now, we can solve for \( r \):

\[
r = \frac{2,080}{10} = 208
\]

Now that we have \( r \), we can find the number of green and yellow Legos:

- Number of red Legos, \( r = 208 \)
- Number of green Legos, \( 3r = 3 \times 208 = 624 \)
- Number of yellow Legos, \( 6r = 6 \times 208 = 1,248 \)

Next, Giovanni trades his yellow Legos for red Legos at a rate of 1 yellow Lego for 1/3 of a red Lego. The total number of new red Legos he can obtain from trading his yellow Legos can be calculated as follows:

\[
\text{New red Legos from yellow} = \frac{1,248}{\frac{1}{3}} = 1,248 \times 3 = 3,744
\]

Now, we will calculate the total number of red Legos he has after the trade. Initially, he has 208 red Legos, and he trades yellow Legos for an additional 3,744 red Legos:

\[
\text{Total red Legos} = 208 + 3,744 = 3,952
\]

Thus, the total number of red Legos Giovanni will have after trading is:

\[
\boxed{3952}
\]