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Standard XII

Mathematics

Types of Linear Programing Problems

The expenses ...

Question

The expenses of a party numbering $43$ were Rs. $229$ ; if each man paid Rs. $10$ , each woman paid Rs. $5$ and each child Rs. $2$ , how many were there of each?

25

5

13

respectively

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35

8

0

respectively

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21

12

10

respectively

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16

5

22

respectively

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Solution

The correct option is D $16$ , $5$ , $22$ respectively
Let the total number of men be x
Let the total number of women be y
Let the total number of children be z
Hence $x + y + z = 43$ and $10 x + 5 y + 2 z = 229$ .
Let the number of women be 5.
Hence
$x + z = 38$
$10 x + 2 z = 204$
Multplying equation i by 2 gives us
$2 x + 2 z = 76$ and $10 x + 2 z = 204$ . Hence $8 x = 128$ or $x = 16$ . Thus $z = 22$ .
Hence $(x, y, z) = (16, 5, 22)$ is a solution to the above problem.

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The expenses of a party numbering 43 were Rs. 229; if each man paid Rs. 10, each woman paid Rs. 5 and each child Rs. 2, how many were there of each?

The expenses of a party numbering $43$ were Rs. $229$ ; if each man paid Rs. $10$ , each woman paid Rs. $5$ and each child Rs. $2$ , how many were there of each?