Solve Diophantine Eq.: 14 Bananas & Pears, £1.52

[Mathematicsresear]

Homework Statement

14 bananas and pears were bought in total by John from the supermarket.
The total cost was £1.52
if Banannas that John purchased cost 5p more than pears, how much did John buy from each fruit?

Homework Equations

The Attempt at a Solution

number of bananas bought = m
cost of bananas bought = n
number of pears bought = 14-m
cost of pears bought = n -5

I am unsure as to what follows

 

[berkeman]

I am unsure as to what follows

Time to write the equation with those variables you've defined and relate that to the total cost...

 

[Mathematicsresear]

Time to write the equation with those variables you've defined and relate that to the total cost...

mn+(14-m)(n-5)=14n+5m = 1.52, so does that mean there are no solutions? This does not make sense.

 

[Ray Vickson]

Homework Statement

14 bananas and pears were bought in total by John from the supermarket.
The total cost was £1.52
if Banannas that John purchased cost 5p more than pears, how much did John buy from each fruit?

Homework Equations

The Attempt at a Solution

number of bananas bought = m
cost of bananas bought = n
number of pears bought = 14-m
cost of pears bought = n -5

I am unsure as to what follows

Please clarify for those of us who are not very familiar with English money: is there nowadays 100 p per pound?

 

[Mathematicsresear]

Please clarify for those of us who are not very familiar with English money: is there nowadays 100 p per pound?

Yes

 

[berkeman]

100 p per pound

mn+(14-m)(n-5)=14n+5m = 1.52

Then 1.52 is not quite correct, right?

 

[berkeman]

mn+(14-m)(n-5)=14n+5m

And I'm not understanding this step...

 

[Mathematicsresear]

Then 1.52 is not quite correct, right?

So, should 1.52 be 152? If so, does that mean I need to multiply all sides by 100?

 

[berkeman]

So, should 1.52 be 152? If so, does that mean I need to multiply all sides by 100?

Just use consistent units on both sides of all equations. Either use pounds or pence on both sides.

 

[Ray Vickson]

Then 1.52 is not quite correct, right?

(1) $m n + (14-m) (n-5) \neq 14 n + 5 m.$
(2) Since you want prices to be in integer numbers of pence, it is convenient to use pence as the monetary unit throughout; otherwise (with the pound as the monetary unit) you would need to find prices that are precise to exactly two decimal places.
(3) When I do it I get three possible solutions to the resulting equation, but two of those are not valid solutions to the original problem