Maths Olympiad Prep

Track / Stage 5 / 69 of 400 #669 of 1964

Problem 669

AIME late
Algebra Difficulty 5.2 Find the answer

4. The newlyweds, the Batterykins, have a combined monthly income of 150,000 rubles. Monthly expenses (food, utilities, mortgage payments, etc.) amount to 115,000 rubles. At the beginning of the year, the family's savings amounted to 45,000 rubles. The family plans to buy new kitchen furniture worth 127,000 rubles using only their own funds. In which month will the family be able to do this? It should be noted that the salary for the month is received on the last day of the month; at that time, the family also makes most of their expenses, including the mortgage payment.

A number or a short expression. Spacing and $ signs are ignored.

Official solution

Answer: April

The family's net monthly income is 150000115000=35000150000-115000=35000 rubles.

The missing amount of funds for the purchase of furniture is 12700045000=82000127000-45000=82000 rubles.

The number of months required to reach this amount is 82000/35000=2.382000 / 35000=2.3. Rounding up, we get 3 months. According to the condition of the problem, the required amount will only be available by the end of March. Therefore, the furniture can be purchased in April.

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