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Example 12: A total of `10000 is distributed among 150 people as prize. A prize is either of `50 or
`100. Find the number of prizes of each type.
Solution: Total number of prizes required = 150 [Q No. of people = 150]

Let the number prizes of `50 be x. Then, the number of prizes of `100 is (150 – x).
∴ Amount spent on x prizes of `50 = `50x
Amount spent on (150 – x) prizes of `100 = `100 (150 – x)
Total amount spent on prizes = `10000

According to the question,
50x + 100 (150 – x) = 10000
⇒ 50x + 15000 – 100x = 10000 ⇒ –50x = 10000 – 15000 = –5000
5000
⇒ x = = 100 So, 150 – x = 150 – 100 = 50
50
Therefore, the number of prizes of `50 is 100 and the number of prizes of `100 is 50.

Practice Time 2A

1. Which of the following equations are linear equations?
3 1
2
( a) x + 4 = 2x − 3 ( b) x + 2 = x + 1 (c) u + = 5 ( d) y – 3 = 3y + 4
2 u
2. Solve each of the following equations and verify the answer.
x 5 3
( a) 5x – 2 = 18 (b) 3x – 3 = 15 (c) 2y + 7 = 19 (d) + = −
3 4 4
5 21 15 x x 3x − 1
7 =
( e) x += ( f) − x 9 ( g) + = 7 ( h) = 11
3
2 2 4 4 3 4
3x x − 6 x − 1
( i) + = 2 ( j) 3 − = 4 ( k) 5(x – 1) = 11
2 4 2
( l) 3(3x – 4) – 2(4x – 5) = 6 (m) 3(x – 1) – 2(3x – 1) = 4
22x − 1) x − 1
(
( n) 4(x + 1) – 8(5 – x) = 3 (o) 5 − 2 = 0
( p) 3x − 4 + 3x + 1 = 7
5 6 15
3. A number is multiplied by 3 and 7 is taken away from the product to get the result 17. What is the
number?
4. The sum of three consecutive multiples of 8 is 888. Find these multiples.
5. The sum of three consecutive integers is 60. Find these three integers.
6. The angles of a triangle are 3x°, (2x + 20)°, and (5x – 40)°. Find the angles.
7. The difference between two numbers is 19. The ratio of these two numbers is 3 : 4. Find these two
numbers.
8. Robert’s father is 4 times as old as Robert. After 5 years, their ages will add to 60 years. Find their
present ages.
9. The length of rectangular hall is 3 metres more than the double of its breadth. If the perimeter of
the hall is 66 metres, what is its length?
10. Three prizes are to be distributed in a quiz contest. The value of the 2nd prize is five-sixths the value
of the first prize and the value of the third prize is four-fifths that of the 2nd prize. If the total value
of the three prizes is `1500, find the value of each prize.

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