a Write the given information as an absolute value inequality and solve it.
B
b Think about the weight of the nickels separately.
A
a Between 193.74g and 209.26g.
B
b Yes, see solution.
Practice makes perfect
a We know that the official weight of a nickel is 5g, but the actual weight can vary from this amount by up to 0.194g. We are asked to find the interval of possible weights for 40 nickels and a 1.5g wrapper. We can write the following absolute value inequality using the given information about a single nickel.
|x-5|≤ 0.194
We can solve the absolute value inequality to determine the interval for the possible weights of a single nickel. Because our distance from the midpoint weight must be less than a certain value, our inequality will be an "and" inequality.
|x-5|≤ 0.194 ⇒ -0.194 ≤ x-5 ≤ 0.194
Let's solve it!
The interval of the possible weights is between 193.74g and 209.26g.
b If each nickel weighs official amount, then the roll's weight is
40*5+1.5=201.5g.
Is it possible for a roll to weigh 201.5g and contain nickels that do not weigh the official amount? Yes, it is possible! Some nickels could weigh more than the official amount and some could weigh less than the official amount. The average of their weights would be the official amount in that case.
