Two kg of tea and 3 kg of sugar cost rupees 39 in january 1997, However in march 1997 the price of the tea increased by 25% and the price of the sugar increased by 20% and the same quantity of tea and sugar cost rupees 48.30. Find their prices in January

Answer: tea = 15 rupees per kg

sugar = 3 rupees per kg

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations with the information given:

"Two kg of tea and 3 kg of sugar cost rupees 39 in january 1997":

2 t + 3 s = 39 (a)

Where:

t = price of 1 kg of tea s = price of 1 kg of sugar

"in march 1997 the price of the tea increased by 25% (1.25) and the price of the sugar increased by 20% (1.20) and the same quantity of tea and sugar cost rupees 48.30. "

2 (t1.25) + 3 (s1.2) = 48.30 (b)

Solving for t in (b)

2t = 39-3s

t = (39 - 3s) / 2

t = 19.5-1.5s

Replacing the value of t in (b)

2 x ((19.5-1.5s) 1.25) + 3 (1.2s) = 48.30

2x (24.375 - 1.875s) + 3.6s = 48.30

48.75 - 3.75s+3.6s = 48.30

48.75-48.30 = 3.75s-3.6s

0.45 = 0.15s

0.45/0.15 = s

3 = s

Replacing the value of s in (a)

2 t + 3 (3) = 39

2 t + 9 = 39

2 t = 39 - 9

2 t = 30

t = 30/2

t = 15

Prices in january:

tea = 15 rupees per kg

sugar = 3 rupees per kg

Feel free to ask for more if needed or if you did not understand something.

x = 15 rupees by kg (price of tea)

y = 3 rupees by kg (price of sugar)

Step-by-step explanation:

Let call " x " the price of kg of tea and " y " the price of kg of sugar, in january of 1997,

then according to problem statement

2*x + 3*y = 39 (1)

But in march prices increased

tea by 25% that means its price in march will be 1.25*x, and the price of sugar will be 1.20*y, finally buying the same quantities now cost 48.30 rupees, then

2 * (1.25*x) + 3 * (1.20*y) = 48.30

2,50*x + 3.60*y = 48.30 (2)

Equations (1) and (2) are a two equation system, we need to solve for x and y

From equation (1) we have y = (39 - 2*x) / 3

Plugging that value in equation (2)

2,50*x + 3.60 * [ (39 - 2*x) / 3] = 48.30

2,50*x + (140,40 - 7,20*x) / 3 = 48.30

7.50*x + 140,40 - 7,20*x = 144,90

0,30*x = 4.50

x = 4.50/0.30

x = 15 rupees

and y = (39 - 2*x) / 3 ⇒ y = (39 - 2*15) / 3

y = (39 - 30) / 3

y = 3 rupees