What's the price of 1 kilogram of bananas? Full question in description.

Question

3 kilograms of bananas cost 5 dollars less then 5 kilograms of apples. 4 kilograms of bananas cost 8 dollars more then 3 kilograms of apples. What's the price of 1 kilogram of bananas?

Answer 1

We'll solve this using a system of equations to represent the situation described:

 

1. Let 'b' represent the cost of 1kg of bananas and 'a' represent the cost of 1kg of apples.

 

2. Now, 3kg of bananas cost $5 less that 5kg of apples.  We can write this equation as:

 

3b = 5a - 5

 

3. Next, we know that 4kg of bananas cost $8 more than 3kg of apples.  We can write this equation as:

 

4b = 3a + 8

 

4. We now have two equations with two variables and can solve by eliminating one of the variables.  First, rewrite each of the equations like this:

 

3b - 5a = -5 (put the two variables together on one side of the equation)

 

4b - 3a = 8

 

5. Let's eliminate the variable a (since the problem asks for the price of the bananas).  To do that multiply each of the first equation's terms by 3 and the second equation's terms by 5.

 

3(3b - 5a) = 3*-5 (remember to multiple all terms in the equation)

 

5(4b - 3a) = 5*8

 

So, we have:

 

9b - 15a = -15

 

20b - 15a = 40

 

Subtract the two equations to get:

 

-11b = -55 (remember that -15a - (-15a) = 0)

 

So, b = -55/-11 = 55/11 = 5; so 1kg of bananas cost $5.00