Subjects algebra

Earnings And Animals Aa58D2

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1. **Problem 1: Earnings and Savings** Celine earns 525 more than Abbas each month. Both spend 1250 each month and save the rest. After 11 months, Celine saved 8250. 2. **Define variables:** Let Abbas's monthly earning be $A$. Then Celine's monthly earning is $A + 525$. 3. **Write the savings equation for Celine:** Savings = Earnings - Spending So monthly savings for Celine = $(A + 525) - 1250$ 4. **Total savings after 11 months:** $$11 \times ((A + 525) - 1250) = 8250$$ 5. **Simplify inside the parentheses:** $$(A + 525 - 1250) = (A - 725)$$ 6. **Substitute and solve for $A$:** $$11 \times (A - 725) = 8250$$ Divide both sides by 11: $$\cancel{11} \times (A - 725) = \frac{8250}{\cancel{11}}$$ $$A - 725 = 750$$ Add 725 to both sides: $$A = 750 + 725 = 1475$$ 7. **Abbas's monthly earning is 1475.** 8. **Find Abbas's yearly earning:** $$1475 \times 12 = 17700$$ --- 9. **Problem 2: Ducks and Cows** There are 3 times as many ducks as cows. Total legs = 400. 10. **Define variables:** Let number of cows be $C$. Number of ducks = $3C$. 11. **Legs per animal:** Cows have 4 legs each. Ducks have 2 legs each. 12. **Write the legs equation:** $$4C + 2(3C) = 400$$ 13. **Simplify:** $$4C + 6C = 400$$ $$10C = 400$$ 14. **Solve for $C$:** $$C = \frac{400}{10} = 40$$ 15. **Find number of ducks:** $$3 \times 40 = 120$$ 16. **Total animals:** $$40 + 120 = 160$$ **Final answers:** - Abbas earns 17700 in a year. - There are 160 animals (ducks and cows) altogether.