Problem Solving (PS) | Re: In a certain game, a large bag is filled with blue, green, purple and

To determine how many purple chips were selected, we start by analyzing the given conditions and breaking down the product of the point values:

1. **Chip Values**:
- Blue chips: 1 point
- Green chips: 5 points
- Purple chips: \(x\) points (where \(5 < x < 11\))
- Red chips: 11 points

2. **Product of Point Values**:
The product of the point values of the selected chips is 88,000.

We can express 88,000 as a product of its primefactors:
\[ 88,000 = 88 \times 1000 \]
\[ 88 = 8 \times 11 = 2^3 \times 11 \]
\[ 1000 = 10^3 = (2 \times 5)^3 = 2^3 \times 5^3 \]
Therefore:
\[ 88,000 = 2^3 \times 11 \times 2^3 \times 5^3 = 2^6 \times 5^3 \times 11 \]

3. **Prime Factor Analysis**:
Each type of chip contributes specific prime factors to the product. Let’s identify the possible factors for each chip:
- Blue chips (1 point): \(1 = 1\) (no contribution to prime factors)
- Green chips (5 points): \(5\)
- Purple chips (\(x\) points): \(x\)
- Red chips (11 points): \(11\)

4. **Factor Contribution**:
We need the factors \(2^6\), \(5^3\), and \(11\).

We know:
- Red chips contribute \(11\).
- Green chips contribute \(5\).

Let’s see how the chips
...

Statistics : Posted by AnkitNandwani1 • on 22 Jan 2012, 17:24 • Replies 34 • Views 42168

---