Question

The maximum number of charms that will fit on a bracelet is $3\left(d-\frac{2}{3}\right)$, where $d$ is the diameter (in centimeters) of the bracelet.

(A). Write and interpret a simplified expression that represents the maximum number of charms on a bracelet.

(B). What is the maximum number of charms that fit on a bracelet that has a diameter of $6$ centimeters?

Answer 1

Step 1: Forming the simplified expression

Given that, maximum number of charms that will fit on a bracelet is $3\left(d-\frac{2}{3}\right)$

$$\begin{gathered} =3\left(d-\frac{2}{3}\right) \\ =3\left(d\right)-3\left(\frac{2}{3}\right)\{Distributiveproperty\} \end{gathered}$$

$=3d-2$

Thus, $(3d-2)$ is the required simplified expression which represents the maximum number of charms on a bracelet.

It can be interpreted from the expression that, maximum number of charms depends on the diamter of the bracelet.

Step 2: Finding the maximum number of charms when diameter is $6$ centimeters

The maximum number of charms that fit on a bracelet that has a diameter of $6$ centimeters can be obtained by just putting $d=6$ in the simplified expression $3d-2$

$$\begin{gathered} =3\left(6\right)-2 \\ =18-2=16 \end{gathered}$$

Hence, $16$ is the maximum number of charms that fit on a bracelet that has a diameter of $6$ centimeters