Exercise 74 Page 611

From the exercise, we know that the weight has to be within

\pm 3 %

of its original weight to be legitimate. If we call the weight of a coin

w,

we can write the following absolute value inequality.

∣ w - 2.5 ∣ \leq 0.03 (2.5)

By removing the absolute value on the left-hand side we get two inequalities. One inequality is less than or equal to

0.03 (2.5),

and the second is greater than or equal to

- 0.03 (2.5) .

∣ w - 2.5 ∣ \leq 0.03 (2.5) ⇓ w - 2.5 \leq 0.03 (2.5) - 0.03 (2.5) \leq w - 2.5

Let's solve these one at the time.

w - 2.5 \leq 0.03 (2.5)

w - 2.5 \leq 0.075

$LHS + 2.5 \leq RHS + 2.5$

w \leq 2.575

Now we will also solve the second inequality.

- 0.03 (2.5) \leq w - 2.5

- 0.075 \leq w - 2.5

$LHS + 2.5 \leq RHS + 2.5$

2.424 \leq w

Rearrange inequality

w \geq 2.424

If we combine the inequalities we can write the solution interval.

2.424 \leq w \leq 2.575

The weight of a coin has to be between

2.424

grams and

2.575

grams if it is legitimate. Therefore, the coin your friend wants to buy is likely a fake.