Question

The cost of 2 kg of apples and 1 kg 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

Answer:

let us consider that price of apple be x

let us consider that price of grapes be y

case1:

2kg apples + 1kg grapes = 160

2x+y=160     ..............eq1

case 2:

4kg apples + 2kg grapes = 300

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

(divide by 2 on both sides)

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

we got two equations 1&3

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

The situation can be represented graphically by plotting these two equations.

consider eq 1

2x+y=160

y=160−2x

let x be 70, 60, 50, 40 in this case

y=160−2x

y=160-2(70)

y=20

y=160-2x

y=160-2(60)

y=40

y=160-2x

y=160-2(50)

y=60

y=160-2x

y=160-2(40)

y=80

the points in this case are (70,20) (60,40) (50,60) (40,80)

consider eq3

2x+y=150

y=150−2x

let x be 65 , 55, 45, 35

y=150−2x

y=150-2(65)

y=20

y=150−2x

y=150-2(55)

y=40

y=150−2x

y=150-2(45)

y=60

y=150−2x

y=150-2(35)

y=80

the points in this case are (65,20) (55,40) (45,60) (35,80)

We can see that the lines do not intersect anywhere, i.e. they are parallel. Hence we can not arrive at a solution.