Subjects algebra

Sale Fridge 010Cf7

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1. **Problem (a):** Saima buys a fridge and a freezer during a 15% off sale. The total amount paid is 57120. The freezer's original price is 40000. Find the fridge's original price. 2. **Formula:** Total price after discount = (Original price of fridge + Original price of freezer) \times (1 - Discount rate) 3. **Step 1:** Let the fridge's original price be $x$. 4. **Step 2:** The total original price is $x + 40000$. 5. **Step 3:** After 15% discount, the price paid is $0.85(x + 40000) = 57120$. 6. **Step 4:** Solve for $x$: $$0.85(x + 40000) = 57120$$ $$\Rightarrow x + 40000 = \frac{57120}{0.85}$$ $$\Rightarrow x + 40000 = 67200$$ $$\Rightarrow x = 67200 - 40000 = 27200$$ 7. **Answer (a):** The fridge's original price was 27200. 1. **Problem (b):** Mr. Rasheed pays a deposit of 60000 and 36 equal monthly payments. Total paid is 127% of 3360000. Find monthly payment. 2. **Formula:** Total paid = Deposit + 36 \times Monthly payment 3. **Step 1:** Calculate total amount paid: $$127\% \times 3360000 = 1.27 \times 3360000 = 4267200$$ 4. **Step 2:** Let monthly payment be $m$. 5. **Step 3:** Set up equation: $$60000 + 36m = 4267200$$ 6. **Step 4:** Solve for $m$: $$36m = 4267200 - 60000 = 4207200$$ $$m = \frac{4207200}{36} = 116866.67$$ 7. **Answer (b):** Monthly payment is 116866.67. 1. **Problem (c):** Divide 600 among A, B, C so that: - 40 more than 2/5 of A's share = - 20 more than 2/7 of B's share = - 10 more than 9/17 of C's share. 2. **Step 1:** Let A's share = $a$, B's share = $b$, C's share = $c$. 3. **Step 2:** Set equal expressions: $$40 + \frac{2}{5}a = 20 + \frac{2}{7}b = 10 + \frac{9}{17}c = k$$ 4. **Step 3:** Express $a$, $b$, $c$ in terms of $k$: $$a = \frac{5}{2}(k - 40)$$ $$b = \frac{7}{2}(k - 20)$$ $$c = \frac{17}{9}(k - 10)$$ 5. **Step 4:** Sum of shares: $$a + b + c = 600$$ $$\Rightarrow \frac{5}{2}(k - 40) + \frac{7}{2}(k - 20) + \frac{17}{9}(k - 10) = 600$$ 6. **Step 5:** Multiply both sides by 18 (LCM of denominators 2 and 9): $$18 \times \left( \frac{5}{2}(k - 40) + \frac{7}{2}(k - 20) + \frac{17}{9}(k - 10) \right) = 18 \times 600$$ $$45(k - 40) + 63(k - 20) + 34(k - 10) = 10800$$ 7. **Step 6:** Expand: $$45k - 1800 + 63k - 1260 + 34k - 340 = 10800$$ $$142k - 3400 = 10800$$ 8. **Step 7:** Solve for $k$: $$142k = 10800 + 3400 = 14200$$ $$k = \frac{14200}{142} = 100$$ 9. **Step 8:** Calculate shares: $$a = \frac{5}{2}(100 - 40) = \frac{5}{2} \times 60 = 150$$ $$b = \frac{7}{2}(100 - 20) = \frac{7}{2} \times 80 = 280$$ $$c = \frac{17}{9}(100 - 10) = \frac{17}{9} \times 90 = 170$$ 10. **Answer (c):** A = 150, B = 280, C = 170. 1. **Problem (d):** Find correct words from jumbled spellings: (i) TEANAIRM (ii) VAGNACEXETRA (iii) VADIELTIONC (iv) PkUNYBARTC (v) TAESROSNС 2. **Step 1:** Unscramble each: (i) TEANAIRM = MARINEAT (likely intended MARINATE) (ii) VAGNACEXETRA = EXTRAVAGANCE (iii) VADIELTIONC = VALIDCTION (likely VALIDATION) (iv) PkUNYBARTC = BANKRUPTCY (v) TAESROSNС = SEASONTS (likely SEASONS) 3. **Answer (d):** (i) MARINATE, (ii) EXTRAVAGANCE, (iii) VALIDATION, (iv) BANKRUPTCY, (v) SEASONS