Question

vincent sells potatoes. He doesn’t sell potatoes my weight or one at a time. he insists on selling them in pairs.his customer graham wants a potato that weighs exactly 200g. Vincent tells him I only have 3 potatoes left. HERe they are A,B and C. A and B together weigh 300g, A and C together weigh 500g, B and C together weigh 400g. You can have any pair of them. Which if any of the potatoes weighs 200g? Which pair of potatoes should graham buy?

Answer 1

By solving a system of equations we will see that the best pair to buy is A and C.

Finding the equations:

Here we have 3 potatoes, A, B, and C. Let's use these variables to define the weight of each potato.

Then, from the given information, we know that:

A + C = 500g

B + C = 400g

A + B = 300g

Then we have a system of equations, to solve it, first we isolate one of the variables in one of the equations. I will isolate A on the first one:

A + C = 500g

A  = 500g - C

Now we can replace that in the third equation, now we have:

B + C = 400g

500g - C + B = 300g

Now we do the same thing, this time I will isolate C.

C = 400g - B

Let's replace this on the other equation:

500g - (400g - B) + B = 300g

500g - 400g + 2*B = 300g

100g + 2*B = 300g

B = (300g - 100g)/2 = 100g

So potato B weighs 100g.

We can use that to find the weight of the other two:

C = 400g - B = 400g - 100g = 300g

A  = 500g - 300g = 200g

What pair should Graham buy?

He wants 200g of potato, so he should buy one pair that includes potato A, which weight exactly 200g. And to get the most of his money, he should buy the pair that contains potato A and that weighs more. So the best pair will be A and C.

If you want to learn more about systems of equations, you can read:

brainly.com/question/13729904