Question 76

1 subtracted from one-third of a number gives 1. Find the number.

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Solution

Let the number be x. Then, one-third of the number = $\frac{1}{3} x .$
According to the question,
$\frac{1}{3} x - 1 = 1 \Rightarrow \frac{1}{3} x = 1 + 1 [t r a n s p o s i n g (- 1) t o R H S] \Rightarrow \frac{1}{3} x = 2 \Rightarrow x = 3 \times 2 [m u l t i p l y i n g b o t h s i d e s b y 3] \Rightarrow x = 6$
Hence, the required number is 6.

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Two subtracted from one-third of a number gives 40. What is the number?

Question 85

Translate each of the following statement into an equation, using x as the variable.

(a) 13 subtracted from twice a number gives 3.

(b) One-fifth of a number is 5 less than that number.

(d) 9 added to twice a number gives 13.

(e) 1 subtracted from one-third of a number gives 1.

40

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