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Word Problems on Elimination Method

In a survey c...

Question

In a survey conducted among 58 ice cream lovers, the data was recorded as a Venn diagram. If the total number of people who eat pistachio flavored ice cream is 25, find the number of people who prefer strawberry over the other flavors.

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Solution

$T o t a l n u m b e r o f p e o p l e w h o p a r t i c i p a t e d i n t h e s u r v e y = 58$

$⟹ 2 x + 3 x + 4 x + y + 2 y + 3 y + x = 58$
$⟹ 10 x + 6 y = 58$

Dividing both side of the equation by 2, we get:

$5 x + 3 y = 29....... E q u a t i o n 1$

Also,

$T o t a l n u m b e r o f p e o p l e w h o e a t p i s t a c h i o f l a v o r e d i c e c r e a m = 25$

$⟹ 3 x + x + y + 2 y = 25$
$⟹ 4 x + 3 y = 25....... E q u a t i o n 2$

Calculating the difference between "Equation 1" and "Equation 2", we get:

$E q u a t i o n 1 - E q u a t i o n 2$

$⟹ x = 4$

$⟹ N u m b e r o f p e o p l e w h o p r e f e r s t r a w b e r r y o v e r t h e o t h e r f l a v o r s = 4 x = 4 \times 4 = 16$

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