Question

* 12 apples and 17 bananas cost Rs 87.25, while 16 apples and 25 bananas cost Rs 119.25How much will 2 bananas and an apple cost?and 1 garlic bread, or 2 pizzas and 4 garlic​

Answer 1

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Let's solve the problem now!!!

Appropriate Question :-

12 apples and 17 bananas cost Rs 87.25, while 16 apples and 25 bananas cost Rs 119.25. How much will 2 bananas and an apple cost?

Solution :-

• Let cost of 1 apple be Rs x

and

• Let cost of 1 Banana be Rs y.

According to statement,

• 12 apples and 17 bananas cost Rs 87.25

$\rm :\longmapsto\:12x + 17y = 87.25 - - - (1)$

According to statement,

• 16 apples and 25 bananas cost Rs 119.25.

$\rm :\longmapsto\:16x + 25y = 119.25 - - - (2)$

On multiply equation (1) by 4 and equation (2) by 3, we get

$\rm :\longmapsto\:48x + 68y = 349 - - - (3)$

and

$\rm :\longmapsto\:48x + 75y = 357.75 - - - (4)$

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

$\rm :\longmapsto\:7y = 8.75$

$\bf\implies \:y = 1.25$

Now,

On substituting the value of y, in equation (1), we get

$\rm :\longmapsto\:12x + 17 \times 1.25 = 87.25$

$\rm :\longmapsto\:12x + 21.25 = 87.25$

$\rm :\longmapsto\:12x = 87.25 - 21.25$

$\rm :\longmapsto\:12x = 66$

$\bf\implies \:x = 5.5$

Thus,

• Cost of 1 apple = Rs 5.5

and

• Cost of 1 Banana be = Rs 1.25

Hence

Cost of 2 bananas and an apple = 2×1.25 + 5.5 = Rs 8.