2. A ham sandwich consists of one slice of ham (7grams) and two slices of bread (25 grams each). You have 1kg of ham and 1kg of bread. You make as many as you can. How many sandwiches did you make? What is the mass of the sandwiches? What is the mass of the ingredients that is left over?
This problem seems like it can be treated almost like a math problem.
We know that one kilogram is equal to one-thousand grams and that one slice of ham is seven grams and two slices of bread are fifty grams total (twenty-five grams each). So you just need to see how many times seven grams goes into one-thousand grams (1000 / 7 = 994 Remainder 6) and how many times 50 grams will go into 1000 grams (1000 / 50 = 20).
The slices of bread come out to be our limiting ingredient. We can only make twenty sandwiches with the bread we're given so that means we need to use up 20 slices of ham.
20 x 7 = 140
1000 - 140 = 860
We're left with 860 grams of ham left and no bread left.
The total weight of our twenty sandwiches is:
20 x (7 + 50) = 1140 grams.
To determine the number of sandwiches you can make, you need to divide the total mass of ham and bread by the combined mass of ham and bread in one sandwich.
1. Calculate the total mass of ham and bread:
- Mass of ham = 1kg = 1000 grams
- Mass of bread = 1kg = 1000 grams
2. Calculate the combined mass of ham and bread in one sandwich:
- Mass of ham = 7 grams
- Mass of bread (2 slices) = 25 grams + 25 grams = 50 grams
3. Divide the total mass of ham and bread by the combined mass in one sandwich:
- Number of sandwiches = (Total mass of ham + Total mass of bread) / (Mass of ham + Mass of bread) in one sandwich
- Number of sandwiches = (1000 grams + 1000 grams) / (7 grams + 50 grams)
- Number of sandwiches = 2000 grams / 57 grams (rounded to the nearest whole number)
The number of sandwiches you can make is approximately 35.
To calculate the mass of the sandwiches made, multiply the number of sandwiches by the combined mass of ham and bread in one sandwich:
- Mass of sandwiches = Number of sandwiches x (Mass of ham + Mass of bread) in one sandwich
- Mass of sandwiches = 35 sandwiches x (7 grams + 50 grams)
- Mass of sandwiches = 35 sandwiches x 57 grams
The mass of the sandwiches made is approximately 1995 grams.
To calculate the mass of the ingredients left over, subtract the mass of the sandwiches made from the total mass of ham and bread:
- Mass of ingredients left over = (Total mass of ham + Total mass of bread) - Mass of sandwiches made
- Mass of ingredients left over = (1000 grams + 1000 grams) - 1995 grams
The mass of the ingredients left over is approximately 5 grams.