Question

3. The cost of 2 kg of apples and 1kg of grapes on a day was found to be * 160. After a
month, the cost of 4 kg of apples and 2 kg of grapes is 300. Represent the situation
algebraically and geometrically.​

Answer 1

Step-by-step explanation:

Let cost each kg of apples = Rs x

Cost of each kg of grapes = Rs y

Given that The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160

So that

2 x + y = 160 … (1)

2x = 160 - y

x = (160 – y)/2

Let y = 0 , 80 and 160 we get

X = (160 – ( 0 ))/2 = 80

X = (160- 80 )/2 = 40

X = (160 – 2* 80 )/2 = 0

X

80

40

0

y

0

80

160

Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300

so we get

4 x + 2 y = 300 … (2)

Divide by 2 we get

2 x + y = 150

Subtract 2x both side we get

Y = 150 – 2 x

Plug x = 0 , 50 , 100 we get

Y = 150 – 2*0 = 150

Y = 150 – 2* 50 = 50

Y = 150 – 2 * (100 ) = - 50

X

0

50

100

Y

150

50

-50

Algebraic representation

2 x + y = 160 … (1)

4 x + 2 y = 300 … (2)

Answer 2

let us consider that price of apple be x & grapes be y

$case1:$

$2x+y=160     ..............eq1$

$case 2:$

$4x+2y=300         .......................eq2$

divide equation 2 on both side by 2

2x+y=150      ..............................eq 3

we got two equations 1&3

2x+y=160 &2x+y=150

then put simanteniously x and y values

2x+y=160                                                2x+y=150

x=50                                                       x=50

100+y=160                                            100+y=150

$y=60$                                                      $y=50$          

$x=30$                                                                $x=30$      

$60+y=160$                                                $60+y=150$    

$y=100$                                                            $y=90$    

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