SOLUTION: to make omelette , 50 gram of butter and 4 to 6 eggs are needed . the mass of each egg is 70 grams , to the nearest 10 gram , but the mass of butter is exact . a) what is the leas

Question 1190070: to make omelette , 50 gram of butter and 4 to 6 eggs are needed . the mass of each egg is 70 grams , to the nearest 10 gram , but the mass of butter is exact .
a) what is the least possible mass of each egg ?
b) between what limit does mass , m grams of omelette lie ?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Part (a)

The mass of each egg is 70 grams, when rounded to the nearest tens place value.

Before rounding, the possible mass of each egg (call it x) is on this interval
The 65 rounds up to 70, but the 75 doesn't round to 70 (it instead rounds to 80), so we exclude 75 from the group.

The least possible mass of each egg is 65 grams.

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Part (b)

m = the mass of the omelette in grams

When considering the smallest mass of each egg (65) and having the lowest number of eggs (4), we'll have 4*65 = 260 grams from the eggs alone. Then add on the mass for the butter (50) and we get 260+50 = 310 grams. This is the lowest m can get.
We can write either or

On the opposite side of the spectrum, if we consider x = 75 grams per egg and use 6 eggs, then 75*6 = 450 grams are from the eggs alone. However, keep in mind that we cannot actually reach this upper bound since x itself cannot be 75.
So more accurately the x < 75 leads to 6x < 450

Then we add on the 50 grams of butter
6x < 450
6x+50 < 450+50
6x+50 < 500
m = 6x+50 is smaller than 500 grams

To summarize the possible range of m, we have this compound inequality

m is somewhere between 310 and 500
m = 310 is possible, but m = 500 is not possible

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