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are given a word problem with the following information: > In an office with **250 employees**, **1/5** of them are male, and **3/5** of the female employees are unmarried. We are told that **70** of the female employees are **married**. We are to find: **How many female employees are unmarried?** --- ### Step 1: Total employees = 250 ### Step 2: Fraction of males = 1/5 So number of **male employees**: \[ \frac{1}{5} \times 250 = 50 \] Therefore, number of **female employees**: \[ 250 - 50 = 200 \] ### Step 3: 3/5 of the female employees are unmarried We are told that 70 female employees are **married**. Let’s check consistency. If total females = 200 And 3/5 are unmarried, then: Number of **unmarried females**: \[ \frac{3}{5} \times 200 = 120 \] Then number of **married females** would be: \[ 200 - 120 = 80 \] But the problem says: "**70** of the female employees are married" This contradicts the math above. Wait — so now we have a **conflict**. The problem says: - 1/5 are male → 50 males → 200 females - 3/5 of female employees are unmarried → implies 120 unmarried, 80 married - But then it says: "**70** of the female employees are married" So 80 married ≠ 70 married → **inconsistency** ### So what’s happening? This suggests a **mistake in the problem statement**, or perhaps **misinterpretation**? Let’s re-read: > In an office with 250 employees, 1/5 of them are male, and 3/5 of the female employees are unmarried. 70 of the female employees are married. How many female employees are unmarried? It gives two different pieces of information about married females: 1. 3/5 of female employees are unmarried → so 2/5 are married → 2/5 * 200 = 80 married 2. But then says 70 are married So one of these must be wrong. Possibility: The problem is testing our ability to **use the 70 married** number to find the answer, and the 3/5 figure is either **incorrect or misleading** — or perhaps a red herring? But that doesn’t make sense — usually in math problems, **all given information is consistent**. Alternatively, maybe we're meant to **ignore the 3/5** and use the 70 married to find unmarried? But then why mention 3/5? Wait — maybe the **3/5** refers to **something else**? Wait, let me check again: > ... 3/5 of the female employees are unmarried. 70 of the female employees are married. So both are stated as facts. But 2/5 of females are married → 80 But 70 is given → contradiction. ### Resolution: Perhaps the 1/5 male is wrong? Wait, maybe we should **use the married number to find total females**, then compute unmarried? Let’s try that approach. Let **F** = number of female employees. We are told: **70 female employees are married** Also, **3/5 of female employees are unmarried** So if 3/5 are unmarried, then **2/5 are married**. So: \[ \frac{2}{5} F = 70 \] Solve for F: \[ F = 70 \times \frac{5}{2} = 175 \] So total female employees = 175 Then total employees = 250 → so male employees = 250 - 175 = 75 But problem says: **1/5 of them are male** 1/5 of 250 = 50 → but we just got 75 males So now **1/5 male** conflicts with **70 married females** and **3/5 unmarried females** So **two statements contradict**: - 1/5 are male → males = 50, females = 200 - 3/5 of females are unmarried → unmarried = 120, married = 80 - But given: married = 70 → contradiction So **the given data is inconsistent**. ### But since the question asks: “How many female employees are unmarried?”, and we are told: > 70 of the female employees are married. And if we assume total females = F, then unmarried = F - 70 But we need to find F. We are also told: 3/5 of female employees are unmarried → so unmarried = (3/5)F So set up equation: \[ F - 70 = \frac{3}{5}F \] Solve: \[ F - \frac{3}{5}F = 70 \] \[ \frac{2}{5}F = 70 \] \[ F = 70 \div (2/5) = 70 \times \frac{5}{2} = 175 \] So **total females = 175** Then unmarried females = 175 - 70 = **105** But then total employees = 250 → males = 250 - 175 = 75 But problem says **1/5 are male** → 1/5 of 250 is 50, not 75 → contradiction. So now we have **two possible interpretations**: ### Possibility 1: Trust "70 married" and "3/5 unmarried" → ignore the 1/5 male Then: - Married females = 70 - Unmarried females = 3/5 of females → implies total females = 175 → unmarried = 105 Answer: **105** ### Possibility 2: Trust "1/5 are male" → so 50 males, 200 females → 3/5 unmarried → 120 unmarried, 80 married But then "70 are married" is wrong. So contradiction. So if we are forced to pick one, since the question is asking for **unmarried females**, and gives **two conflicting ways to compute**, which one do we use? In most math problems, if a direct number is given (70 married), and a fraction is given (3/5 unmarried), and they conflict with a third fact (1/5 male), we usually **use the direct number** and the proportion to find the unknown, **and assume the fractional proportion takes precedence over the total**? Or vice versa? But note: the problem says **"70 of the female employees are married"** — this is a specific count. It also says **"3/5 of the female employees are unmarried"** — this is a proportion. But if total females is not yet known, we can use the proportion and the absolute to solve for total. That’s standard algebra. We have: Let F = number of female employees. 3/5 F are unmarried → then 2/5 F are married We are told: 2/5 F = 70 → F = 175 So number unmarried = 3/5 * 175 = 105 The statement "1/5 of them are male" must then be **wrong** — or it's a trick. But maybe the problem meant **1/5 are female**? That would make more sense if we get 50 females... but 50 females, 70 married? Impossible. Wait — if 1/5 are female → F = 50 → then 3/5 of them unmarried → 30 unmarried → married = 20, not 70 → even worse. Alternatively, maybe "1/5 of **female** employees are male"? Nonsense. So the only consistent interpretation is: **Ignore the "1/5 are male" as erroneous or misstated**, and use: > 3/5 of female employees are unmarried, and 70 are married → find unmarried So: Let F = number of females Married = 70 = 2/5 F → F = 175 Unmarried = 175 - 70 = 105 Or 3/5 * 175 = 105 So answer is **105** Alternatively, maybe the problem meant: 1/5 are **married**? No, it says male. Another possibility: Perhaps “1/5 of them are male” refers to something else? Unlikely. ### Conclusion The only way to resolve the contradiction without inconsistency is to use the **married = 70** and **3/5 unmarried** to compute total females, and accept that the "1/5 are male" is **likely a mistake** in the problem. Thus, **number of unmarried female employees is 105** ✅ Final Answer: **105** But let me check: is there a way to make 1/5 male AND 70 married female? Total employees: 250 If males = 1/5 * 250 = 50 → females = 200 Then 70 married → unmarried females = 200 - 70 = 130 Then fraction unmarried = 130/200 = 13/20, not 3/5 (which is 12/20) So 13/20 ≠ 3/5 → so **can’t satisfy both** So the problem contains **inconsistent data**. In such cases, typically, if two quantitative pieces of info are in conflict, and one is a direct count and the other is a proportion, we use the direct count to compute, and see if it violates the proportion. But here, since the question is **“How many are unmarried?”**, and two pieces of info are given about females: one is a direct number (70 married), and one is a proportion (3/5 unmarried), we use **both** to find the actual value. So solving: Let unmarried = U Married = 70 Then total females F = U + 70 Also, U = (3/5) F So: U = (3/5)(U + 70) Multiply both sides by 5: 5U = 3(U + 70) 5U = 3U + 210 2U = 210 U = 105 So **105** is the answer from internal consistency of the two female-related statements. The male statement contradicts, but since it doesn’t directly relate to the question (“female unmarried”), and the question is answerable without relying on it, we go with 105. So, final answer: **105** --- ### ✅ Answer: \boxed{105}

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