A company sells two products: A and B. Product A costs $50, and 40% of sales are Product A. Product B costs $70. If total revenue from 100 units sold is $6,500, how many units of Product B were sold?

["How Many Units of Product B Were Sold? Solving a Sales Revenue Problem", "Understanding sales data is essential for any business, especially when pricing and demand vary between products. In this case, a company sells two main products—Product A and Product B—with distinct pricing and sales contributions. We’ll break down how to determine the number of units sold for Product B, given a total revenue of $6,500 from 100 units.", "### The Setup", "- Product A price: $50 per unit, accounting for 40% of total units sold.\n- Product B price: $70 per unit, representing the remaining 60% of sales.\n- Total units sold: 100\n- Total revenue: $6,500", "We aim to find how many units of Product B were sold.", "### Step-by-Step Analysis", "Let the number of units sold for Product A be $ x $. Since 40% of sales are Product A, this means:", "$$\nx = 0.4 \ imes 100 = 40\n$$", "Therefore, the number of units sold for Product B is the remainder:", "$$\n100 - x = 100 - 40 = 60\n$$", "But to verify, let’s confirm with revenue:", "- Revenue from Product A: $ 40 \ imes 50 = 2,000 $\n- Revenue from Product B: $ (100 - x) \ imes 70 = (60) \ imes 70 = 4,200 $", "Total revenue:\n$$\n2,000 + 4,200 = 6,200\n$$", "Wait — this totals $6,200, not $6,500. The discrepancy indicates our initial assumption based only on percentage may conflict with total revenue — so let’s reframe the problem algebraically.", "### Let’s Use Variables to Solve Exactly", "Let $ a $ = number of units sold of Product A\nLet $ b $ = number of units sold of Product B", "Given:\n1. $ a + b = 100 $\n2. $ 50a + 70b = 6,500 $\n3. Also, $ a = 0.4(a + b) = 0.4 \ imes 100 = 40 $ — confirmed earlier", "Using $ a = 40 $, substitute into the revenue equation:\n$$\n50(40) + 70b = 6,500\n\Rightarrow 2,000 + 70b = 6,500\n\Rightarrow 70b = 4,500\n\Rightarrow b = \frac{4,500}{70} = 64.2857...\n$$", "This non-integer result suggests a conflict — but wait: the problem says “40% of sales are Product A,” which applies to units, but revenue calculation with exact 100 units and $6,500 revenue must align.", "Let’s instead interpret carefully: “40% of sales” means 40% of units are A, so $ a = 40 $, $ b = 60 $, but revenue is only $6,200 — so total revenue of $6,500 implies there may be more data, or pricing reflects weighted average.", "But the key is: If Product A is 40% of units, and total units = 100, then $ a = 40 $, $ b = 60 $ exactly — no rounding needed.", "But revenue from $ a = 40, b = 60 $ is $50×40 + $70×60 = $2,000 + $4,200 = $6,200, not $6,500. So either the percentages or revenue includes weighted averages — but problem states “40% of sales are Product A” — likely meaning units.", "Recheck: total revenue = $6,500 from 100 units, price A=$50, B=$70, and 40% of units are A.", "Let $ a = 0.4 × 100 = 40 $, $ b = 60 $\nRevenue: $ 40×50 = $2,000 $, $ 60×70 = $4,200 $, total: $6,200", "But $6,200 ≠ $6,500 — contradiction.", "Thus, reconsider assumption: perhaps “40% of sales” refers to revenue, not units?", "But problem says: “40% of sales are Product A” — inconsistent with revenue unless cost includes margin, but unlikely.", "Alternative: maybe “sales” means units by count — so 40% of 100 units = 40 units of A.", "But revenue doesn’t match — so perhaps the 40% applies to revenue share, not units? But problem states “sales,” implying units.", "Wait — error in initial assumption?", "Let’s set up equations without assuming percentage:", "Let $ a $ = units of A, $ b $ = units of B\nGiven:\n$ a + b = 100 $\n$ 50a + 70b = 6,500 $", "From first equation: $ a = 100 - b $", "Substitute:\n$$\n50(100 - b) + 70b = 6,500\n\Rightarrow 5,000 - 50b + 70b = 6,500\n\Rightarrow 20b = 1,500\n\Rightarrow b = 75\n$$", "So $ b = 75 $ units of Product B were sold.", "Now verify:\n$ a = 100 - 75 = 25 $ units\nRevenue: $ 25×50 = 1,250 $, $ 75×70 = 5,250 $, total: $6,500 — correct.", "But what about the 40% rule?", "If 40% of sales are A — meaning 40% of total units? Then $ a = 40 $, $ b = 60 $, revenue = $2,000 + $4,200 = $6,200 ≠ $6,500.", "So the 40% cannot be about unit count under given sales and revenue.", "Therefore, unless specified otherwise, interpret the 40% as a revenue-weighted or volume-weighted contribution, but the only consistent solution with revenue is $ b = 75 $.", "Hence, the “40% of sales are Product A” must refer to unit count, but the revenue implies different proportions — or the problem intends the % to guide but not override the revenue.", "But practically, the revenue data supersedes the partial unit claim — so re-evaluate using both.", "Only consistent integer solution satisfying revenue and total units is $ b = 75 $. So the 40% likely emphasizes A’s dominance but is not strictly enforced by unit count.", "Alternatively, correction: perhaps “40% of sales” means 40% of total units, but then revenue doesn’t match — so maybe typo? Or misinterpret “sales”?", "But since math confirms $ b = 75 $ solves revenue, and $ a = 25 $ is 25% of units (not 40%), the 40% must refer to revenue contribution, not unit count.", "But problem says “40% of sales are Product A” — standard interpretation is unit count.", "To resolve, assume the 40% refers to unit proportion, but data inconsistency implies error — unless sales refers to something else.", "But given the revenue and total units, only $ b = 75 $ satisfies:\n$ a + b = 100 $, $ 50a + 70b = 6,500 $ → $ b = 75 $", "Thus, the number of units of Product B sold is 75.", "### Final Answer", "Despite the 40% unit claim, the only value satisfying total revenue and total units is 75 units of Product B. The discrepancy suggests “40% of sales” may describe early demand trends or market share, not current sales proportions — but mathematically, the revenue confirms $ b = 75 $.", "How many units of Product B were sold? → 75", "This illustrates how revenue and unit data must be aligned — and when resolved, the math confirms Product B dominates in volume in this scenario.", "---", "SEO Meta Tags (for publication):\nProduct A revenue, Product B price, calculate units sold, solve sales revenue problem, 100 units sold total, $6,500 revenue, $50 and $70 pricing, 40% of units A — revenue reconciles to 75 units B", "Keywords: Product A revenue, Product B pricing $70, sales units calculation, 100 units sold total, solving revenue equation, project revenue analysis, how many units of Product B sold"]