Denoting the mass of old potatoes he buys by m kg, write doen an expression for the total cost of Joe's potatoes. What mass of new potatoes does he buy?

Question

Joe buys 18kg of potatoes. Some of these are old potatoes at 22c per kilogram, the rest are new ones at 36c per kilogram...... Joe pays with a $5 note and receives 20c change.

Answer 1

First, we know that he spent $4.80 (5-20c), we know the total mass of the potatoes he bought, and we know the price of each type of potato.

 

We are dealing with 2 equations here:

 

o+n=18 (for "old plus new equals 18")

 

and 

 

0.22o + 0.36n = 4.80 (for the prices of the old and new potatoes).

 

What you need to do now is combine the equations. I did this by multiplying the first equation by 0.22:

 

        o + n = 18

x                0.22

______________

 

(you have to multiply 0.22 to both sides of the equation, including 18)

 

What you end up with is this new equation:

 

0.22o + 0.22n = 3.96

 

You then subtract this equation from the other equation like this:

 

       0.22o + 0.36n = 4.80

    - (0.22o + 0.22n = 3.96)

_______________________

             0  + 0.14n = 0.84

 

So we can see that we have completely cancelled out o, leaving us with only n to deal with.

 

Now our new equation is:

 

0.14n = 0.84

 

solving for n, we get

 

n = 6

 

and that is the mass of the new potatoes he buys.

Answer 2

Jasmine:

 

Mass m  of old potatoes cost Joe 22m cents. Since Joe buys a total of !8 kg potatoes, he buys (18 -m) kg of new potatoes. The cost of new potatoes is 36(18-m) cents. 

 

His total cost is 22m + 36(18-m) cents. 

 

We are given that the total cost in $5 - 20 cents = 480 cents. Therefore

 

22m + 36(18 - m) = 480, that is, 22m + 648 - 36m = 480.  14m = 168.  m = 12, 18-m = 6. 

 

He buys 6 kg of new potatoes.

 

Dattaprabhakar (Dr. G.)