+36 Ali ears a fixed monthly salary. In June, he spent 1/3 of his salary on a table and 5/6 of his remaining salary on a television.
(a) What fraction of Ali's salary was spend on the television?
(b) After buying the table and television, Ali had $360 left. Then, he spent $336 to buy a total of 20 plates and bowls. Each bowl cost $27 while each plate cost $10. What fraction of Ali's salary was spent on the plates?
+929 a) Fraction of Salary Spent on Television
Let Ali's initial salary be 'x'
Amount spent on the table: (1/3)x
Remaining salary after buying the table: x - (1/3)x = (2/3)x
Amount spent on the television: (5/8) * (2/3)x = (5/12)x
Therefore, the fraction of Ali's salary spent on the television is 5/12.
b) Fraction of Salary Spent on Plates
Remaining money after buying the table and television: $350
Total cost of plates and bowls: $316
Let 'p' be the number of plates and 'b' be the number of bowls.
p + b = 20
10p + 25b = 316
Solve the system of equations:
From the first equation, p = 20 - b
Substitute 'p' in the second equation: 10(20 - b) + 25b = 316
200 - 10b + 25b = 316
15b = 116
b = 7.73 (Since the number of bowls must be a whole number, we can round down to 7)
p = 20 - 7 = 13
Cost of plates: 13 plates * $10/plate = $130
Total salary: $350 (remaining) + $316 (spent on plates and bowls) = $666
Fraction of salary spent on plates: $130 / $666 ≈ 0.1955
Therefore, the fraction of Ali's salary spent on plates is approximately 0.1955 or about 19.55%.
