A team composed of Boris and Fiona sold souvenir programs for $3 each at two performances of a local band...

Phase 1: Owning the Dataset

Visual Representation

Let's organize the sales data in a table:

We know:

• Programs cost \(\$3\) each
• Total revenue = \(\$1{,}500\)
• Total programs sold = \(\$1{,}500 ÷ \$3 = 500\) programs

Setting Up Variables

Let's denote:

• Boris's afternoon sales = \(\mathrm{p}\)
• Boris's evening sales = \(\mathrm{q}\)
• Fiona's afternoon sales = \(\mathrm{r}\)
• Fiona's evening sales = \(\mathrm{s}\)

Phase 2: Understanding the Question

Key Constraints

From the passage:

1. "Boris sold as many programs at the afternoon performance as Fiona did at the evening performance"
   • This means: \(\mathrm{p} = \mathrm{s}\)
2. "Fiona sold as many programs in the afternoon as Boris did in the evening"
   • This means: \(\mathrm{r} = \mathrm{q}\)

Updating Our Visual

With these constraints, our table becomes:

Notice the symmetric pattern! Both Boris and Fiona sell the same total number of programs.

Phase 3: Finding the Answer

Calculating the Values

Since the total programs sold = 500:

• \(2(\mathrm{p} + \mathrm{q}) = 500\)
• \(\mathrm{p} + \mathrm{q} = 250\)

Therefore:

• X (Boris's total) = \(\mathrm{p} + \mathrm{q} = 250\)
• Y (Team's afternoon total) = \(\mathrm{p} + \mathrm{q} = 250\)

Verification

Let's verify this makes sense:

• Boris sold 250 programs total
• Fiona sold 250 programs total
• Combined: \(250 + 250 = 500\) programs ✓
• Revenue: \(500 × \$3 = \$1{,}500\) ✓

Phase 4: Solution

Final Answer:

• X = 250
• Y = 250

Both values equal 250, which perfectly satisfies all the given constraints. The symmetric nature of the problem (where each person's afternoon sales equal the other's evening sales) creates this elegant result where both the individual total and the afternoon total are the same.