Is the weight of the ball greater than the minimum acceptable weight?
A
a
Equality: |x-430|=20
Minimum Weight: 410 grams Maximum Weight: 450 grams
B
b
No, see solution.
Practice makes perfect
a
The recommended weight of a soccer ball is 430 grams. The difference between the recommended weight and the actual weight x can be expressed as x- 430. Since we are not interested in the sign, we will only consider an absolute value of the expression.
|x- 430|In the exercise we are told that the weight can vary up to 20 grams. Since we are looking for the minimum and maximum weights of the ball, we need to find for what x the expression above is equal to 20.
|x- 430|= 20
To solve for x, we will split our absolute value equation into two separate cases.
The weight cannot be less than 410 grams, and it cannot be more than 450 grams.
b
We know that the weight of a ball that was originally 423 grams decreased by 16 grams. To find out whether the weight is acceptable, we need to determine if it falls between the minimum and maximum acceptable weight. First, let's find its current weight.
423 - 16 = 407
The ball now weighs 407 grams. In Part A we found that the minimum acceptable weight is 410 grams, which is more than our ball weighs.
407 < 410
Therefore, the ball weighs less than the minimum acceptable weight and is not acceptable.
