Sean bought 5 lemons and 4 limes for $4.15. At the same prices, Kim bought 3 lemons and 9 limes for $6.45. Find the price per lemon and the price per lime.

Question

Sean bought 5 lemons and 4 limes for $4.15. At the same prices, Kim bought 3 lemons and 9 limes for $6.45. Find the price per lemon and the price per lime.

Answer 1

Let x = price of a lemon

     y = price of a lime

 

Then 5x + 4y = 4.15

        3x + 9y = 6.45

 

Multiply equation 1 by 3 and equation 2 by -5 to obtain:

 

15x + 12y = 12.45

-15x - 45y = -32.25

 

Adding these equations, we get -33y = -19.8.

So, y = -19.8/(-33) = $0.60.

 

Substitute 0.60 for y into either one of the given equations to get

x = $0.35 .

 

So, one lemon costs $0.35 and one lime costs $0.60.