Question

(2) Kantabai bought 1 kg tea and 5 kg sugar from a shop. She paid 50 as
return fare for rickshaw. Total expense was 700 Then she realised that to
ordering online the goods can be bought with free home delivery at Same
price. So next month she placed the order online for 2 tea and 7 kg sugar
She paid 880 for that. Find the rate of sugar and tea per kg.​

Answer 1

Let price of 1 kg tea = x

Let price of 1 kg sugar = y

3/2x + 5y + 50 = 700

3x + 10y = 1300.....(1)

2x + 7y = 880......... (2)

Multiply eq(1) by 2 and eq(2) by 3

6x + 20y = 2600......(3)

6x + 21y = 2640......(4)

Subtract eq(3) from eq(4)

y = 40

Put value of y = 40 in eq(1)

3x + 10*40 = 1300

3x = 1300 - 400

3x = 900

x = 300

Price of 1 kg tea = Rs 300

Price of 1 kg sugar = Rs 40

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Answer 2

Answer:

The rate of 1 kg of tea is ₹ 300.

The rate of 1 kg of sugar is ₹ 40.

Step-by-step-explanation:

NOTE: Kindly refer to the attachment first.

Let the rate of 1 kg of tea be ₹ x.

And the rate of 1 kg of sugar be ₹ y.

The cost of 1.5 kg of tea = ₹ 1.5 x

[ $\because\sf\:1\frac{1}{2}\:=\:1.5$ ]

Also, the cost of 5 kg of sugar = ₹ 5 y.

Rickshaw fare = ₹ 50.

From the first condition,

$\sf\:1.5\:x\:+\:5\:y\:+\:50\:=\:700\\\\\implies\sf\:1.5\:x\:+\:5\:y\:=\:700\:-\:50\\\\\implies\sf\:1.5\:x\:+\:5\:y\:=\:650\\\\\implies\sf\:3\:x\:+\:10y\:=\:1300\:\:\:-\:-\:-\:[\sf\:Multiplying\:both\:sides\:by\:2\:]\:\:(1)$

The cost of 2 kg of tea = ₹ 2x.

And the cost of 7 kg of sugar = ₹ 7y.

From the second condition,

$\sf\:2x\:+\:7y\:=\:880\:\:\:-\:-\:-\:(2)$

Multiplying equation ( 1 ) by 2 and equation ( 2 ) by 3, we get,

$\sf\:3x\:+\:10y\:=\:1300\:\:-\:-\:(1)\:\times\:2\\\\\implies\sf\:6x\:+20y\:=2600\:\:-\:-\:-\:(3)\\\\\implies\sf\:2x\:+\:7y\:=\:880\:\:-\:-\:(2)\:\times\:3\\\\\implies\sf\:6x\:+\:21y\:=\:2640\:\:-\:-\:(4)$

Subtracting equation ( 3 ) from equation ( 4 ), we get,

$\sf\:\cancel{6x}\:+\:21y\:=\:2640\:\:-\:-\:-\:(4)\\\\\sf\:-\:\cancel{6x}\:+\:20y\:=\:2600$

$\sf\boxed{\sf\:y\:=\:40}$

Substituting $\sf\:y\:=\:40$ in equation ( 2 ), we get,

$\sf\:2x\:+\:7y\:=\:880\:\:-\:-\:-\:(2)\\\\\implies\sf\:2x\:+\:7\:\times\:40\:=\:880\\\\\implies\sf\:2x\:+\:280\:=\:880\\\\\implies\sf\:2x\:=\:880\:-\:280\\\\\implies\sf\:2x\:=\:600\\\\\implies\sf\:x\:=\:\frac{600}{2}\\\\\implies\sf\boxed{\sf\:x\:=\:300}$

Ans.: The rate of 1 kg of tea ( x ) = ₹ 300.

The rate of 1 kg of sugar ( y ) = ₹ 40.

Additional Information:

1. Linear Equations in two variables:

The equation with the highest index

( degree ) 1 is called as linear equation. If the equation has two different variables, it is called as 'linear equation in two variables'.

The general formula of linear equation in two variables is

$\sf\:ax\:+\:by\:+\:c\:=\:0$

Where, a, b, c are real numbers and

a ≠ 0, b ≠ 0.

2. Solution of a Linear Equation:

The value of the given variable in the given linear equation is called the solution of the linear equation.

3. Stpes to solve word problems based on linear equations in two variables:

1. Understand the information given in the problem.

2. Identify the required quantities given and to find.

3. Convert the words into symbols by using variables ( x, y, a, b ).

4. Solve the equations formed step-by-step.

5. Write the value of variables ( solution of equation ) in words ( as asked in the question ).