Question

Consider the following problem. You tell your greengrocer that you have £1 to spend on apples and bananas. He says you could buy four apples and three bananas or you could buy six apples and two bananas. In either case, you would get no change from £1, i.e. the bill is exactly 100p.

Is it possible to tell from this what the price of an apple is? What about the price of a banana?​

Answer 1

apple: £0.10 banana: £0.20

Explanation:

x = apples

y = bananas

6x + 2y = 1 (because overall there were 6 apples and 2 bananas)

the other equation would be:

4x + 3y = 1 (because overall for the other one there were 4 apples and 3 bananas)

put in slope int. form

3y = -4x + 1

y = -4/3x + 1/3

2y = -6x +1

y = -3x + 1/2

since they both equal y, they equal each other:

-3x + 1/2 = -4/3x + 1/3

multiply the whole equation by 6 so only integers are left:

-18x + 3 = -8x + 2

now simplify for x:

3 = 10x + 2

1 = 10x

x = £0.10

apples are £0.10 each

to find bananas:

6(.10) + 2y = 1

.60 +2y = 1

2y = .40

y = £0.20

bananas are £0.20 each

Answer 2

I can tell by using a system of equations (not sure if you’ve learned this) basically you make two equations which would be 4x+3y=1 and 6x+2y=1 and (x is apples and y is bananas) graph these by hand or on a website such as Desmos by entering the equations. Where the lines intersect is the price of each, your first number will be your cost for an apple while the other will be for the cost of a banana. I’m not sure if this is how you should be finding your answer but it’s a possible way.