Maths Week Scotland 2023 - Problem 2 - The farmer's weight

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Problem 2 - The farmer's weight

Problem 2 is all about a farmer and his food.

Maths teacher Chris Smith and pupils from Grange Academy are here to explain.

The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.

So here's the challenge:

Calum is a farmer and he farms chickens and turkeys.

One December morning Calum takes an egg for breakfast and then he gets a turkey ready for the oven for Christmas dinner.

Calum’s weight is:

  • 10 x that of the turkey
  • 1000 x that of the egg

The turkey weighs 6930g more than the egg.

Can you work out how much Calum weighs?

Calum is standing at kitchen table with egg and turkey. Calum weighs 10x turkey, 1000x egg and a turkey weighs 6930g more than the egg.
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Need a hint?

  • Can you use ratios, fractions or percentages to help you find the answer?
  • Can you work out how many eggs weigh the same as the turkey?
  • Can you work out the weight of one egg?
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Solution

Worked out the answer? Here's how you can do it.

10 turkeys weigh the same as 1000 eggs so 1 turkey weighs the same 100 eggs

Step 1

We know how Calum's weight compares to the turkey and the egg:

Calum = 10 x turkey

Calum = 1, 000 x egg

We can use this to work out how the weight of the turkey and the egg compare:

Calum = 10 x turkey = 1, 000 x egg

=> 10 x turkey = 1, 000 x egg

=> turkey = 100 x egg

10 turkeys weigh the same as 1000 eggs so 1 turkey weighs the same 100 eggs
One egg equals 70g

Step 2

We know that the turkey = 6, 930 g + egg

And we now know that turkey = 100 x egg

So we can swap this information into the first equation:

100 x egg = 6, 930 g + egg

Take one egg away from each side:

99 x egg = 6, 930g

Divide both sides by 99:

egg = 70 g

One egg equals 70g
Calum weighs the same as 10 turkeys, which means he weighs 70kg.

Step 3

We can now use the weight of one egg to work out what the turkey weighs:

turkey = 100 x 70 g

= 7,00 g

=7 kg

The question is what Calum weighs and we can work this out:

Calum = 1,000 x 70 g

= 70, 000g

= 70 kg

The answer is, Calum weighs 70 kg.

Calum weighs the same as 10 turkeys, which means he weighs 70kg.

Try out all the daily challenges from Maths Week Scotland 2023.

Maths Week Scotland 2023

Try out all the daily challenges from Maths Week Scotland 2022.

Maths Week Scotland 2022

Want more maths challenges? Here are all the problems from 2021.

Maths Week Scotland 2021

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