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.
CHRIS: This cracking problem is all about a farmer and his food.
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 ten times that of the turkey and a thousand times that of the egg. The turkey weighs six thousand nine hundred and thirty grams more than the egg. Can you work out how much Calum weighs?
So what are the three things that we care about in this question?
PUPIL: The egg
CHRIS: Egg
PUPIL: Turkey
CHRIS: Turkey and?
PUPIL: Calum
CHRIS: Calum. Right okay.
PUPIL: Can you use ratios, fractions or percentages to help you find the answer?
CHRIS: How does Calum compare to the turkey?
PUPIL: He's ten鈥
CHRIS: He's ten ten times heavier, right okay.
PUPIL: Can you work out how many eggs weigh the same as the turkey?
CHRIS: The turkey is one hundred times the size of the egg. And he's a thousand times heavier than the egg.
PUPIL: Can you work out the weight of one egg?
PUPIL: Good luck.
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鈥檚 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?
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?
Solution
Worked out the answer? Here's how you can do it.
CHRIS: This problem was all about comparing different weights.
We know that Calum's weight is ten times that of the turkey and a thousand times that of the egg. So that means that ten turkeys weigh the same as a thousand eggs.
So one turkey weighs the same as one hundred eggs.
We also know that the turkey weighs six thousand nine hundred and thirty grams more than one egg. That means six thousand nine hundred and thirty grams is the weight of ninety nine eggs.
One egg weighs six thousand nine hundred and thirty divided by ninety nine, which is seventy grams. The turkey weighs a hundred times that, which is seven thousand grams or seven kilograms and Calum weighs ten times that. So our answer is that Calum weighs seventy kilograms.
There's your seventy, that's the seventy.
How did you get on?
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
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
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.
Maths Week Scotland 2023. list
Try out all the daily challenges from Maths Week Scotland 2023.
Maths Week Scotland 2022. list
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