SOLUTION: a man's weekly pay is x naira. he spend half of his pay on food and one-third on rent. a] express the amount he spends on food in terms of x. b] express the amount he spends on ren

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: a man's weekly pay is x naira. he spend half of his pay on food and one-third on rent. a] express the amount he spends on food in terms of x. b] express the amount he spends on ren      Log On


   

Question 1033436: a man's weekly pay is x naira. he spend half of his pay on food and one-third on rent. a] express the amount he spends on food in terms of x. b] express the amount he spends on rent in terms of x. c] find the weekly pay if he spends a total of 1600 naira on food and rent.
Answer by Theo(13342) About Me  (Show Source):
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the man's weekly pay is x naira.

he spends half on food and one third on rent.

cost of food = 1/2 * x.

cost of rent = 1/3 * x.

1/2 * x + 1/3 * x = 1600.

convert to a common denominator of 6 to get:

3/6 * x + 2/6 * x = 1600.

combine like terms to get 5/6 * x = 1600

divide both sides of this equation by 5/6 to get x = 1600 / (5/6).

that's the same as x = 1600 * (6/5) which makes x = 1920.

his salary is 1920.
he spends half on food.
one half of 1920 = 960.
he spend one third on rent.
one third of 1920 = 640.
total spent on rent and food is 960 + 640 = 1600.

number look good.

his weekly pay is 1920 naira.