Stretch Your Thinking Toby is choosing from two bead
art projects. Project A uses equal numbers of red, black,
and green beads totaling 825 beads. Project B uses equal
numbers of black, blue, green, and yellow beads totaling
1,020 beads. Toby has 260 green beads and doesn’t want
to purchase more green beads. Explain which of the two
bead projects Toby should choose.

Question

UpStudy AI · Accepted Answer

1. **Project A Analysis:**

- Project A uses three colors with equal numbers of beads (red, black, and green) totaling $$825$$ beads.
   - The number of beads for each color is:
     $$
     \frac{825}{3} = 275.
     $$
   - This project requires $$275$$ green beads.

2. **Project B Analysis:**

- Project B uses four colors with equal numbers of beads (black, blue, green, and yellow) totaling $$1020$$ beads.
   - The number of beads for each color is:
     $$
     \frac{1020}{4} = 255.
     $$
   - This project requires $$255$$ green beads.

3. **Comparing with Toby's Resources:**

- Toby has $$260$$ green beads.
   - Project A requires $$275$$ green beads, which is more than available.
   - Project B requires $$255$$ green beads, which is within the available amount.

4. **Conclusion:**

Toby should choose **Project B**, because it requires only $$255$$ green beads, which he can supply with his available $$260$$ green beads.
Toby should choose Project B because it requires 255 green beads, which he has enough of, whereas Project A needs 275 green beads, more than he currently possesses.

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