Find how much it would therefore cost to buy 1kg of apples and 1kg of bananas. Please help

Question

Jimmy buys 4kg of apples and 3kg of bananas from the local grocery score for $19.60. Julie buys
2kg of apples and 5kg of bananas from the same store for $18.65. Assuming the prices of apples
and bananas (per kg) were the same for both purchases, find how much it would therefore cost to
buy 1kg of apples and 1kg of bananas.

Answer 1

Let a = $/kg apples

Let b = $/kg bananas

 

4a + 3b = 19.6 _______ eqn 1

2a + 5b = 18.65 ______ eqn 2

 

Multiply eqn 2 by -2 and add equations

 

4a + 3b = 19.6

-4a -10b = -37.3

----------------------

      -7b = -17.7

        b = $2.53 per kg

 

4a + 3b = 19.6

4a + 3(2.53) = 19.6

4a + 7.59 = 19.6

4a = 19.6 - 7.59 = 12.01

a = 12.01/4

a = $3 per kg

 

1 kg apples plus 1 kg bananas 

= 3 + 2.53 = $5.53