Chapter 1.2, Problem 36HP

Solution

(a)

If 1 inch = 2.54 centimeters, write and evaluate an expression to find the number of centimeters in 200 inches.

  $508\text{cm}$

GIVEN:

Leah bought two packages of special decorative trim for a craft project. One package contains 350 centimeters of trim. The second package contains 200 inches of trim. If 1 inch = 2.54 centimeters.

Calculation:

In order to write and evaluate an expression to find the number of centimeters in 200 inches, if 1 inch=2.54 centimeters, first multiplying 2.54 to 200 because 1 inch is equal to 2.54 and there is total 200 inches to simplify further as shown below:

  $\begin{array}{l}200\times \left(2.54\right)\\ =508\text{cm}\end{array}$

So, there are 508cm in 200 inches.

(b)

Find the total number of centimeters of trim in the two packages.

  $858\text{cm}$

GIVEN:

Leah bought two packages of special decorative trim for a craft project. One package contains 350 centimeters of trim. The second package contains 200 inches of trim.

Calculation:

In order to find the total number of centimeters of trim in the two packages, first adding the one package, that is 350cm and the second package contain 200 inches which has 508cm, to simplify further as shown below:

  $\begin{array}{l}350+508\\ =858\text{cm}\end{array}$

So, the total number of centimeters of trim in the two packages is 585cm.

(c)

How many packages of trim containing 90 inches each will Leah need to buy to have about the same amount of trim from part b. explain.

  $4\text{packages}$

GIVEN:

Leah bought two packages of special decorative trim for a craft project. One package contains 350 centimeters of trim. The second package contains 200 inches of trim.

Calculation:

In order to find how many packages of trim containing 90 inches each will Leah need to buy to have about the same amount of trim from part b, first to find how many centimeters in 90 inches multiplying 90 to 2.54 because 1 inch is equal to 2.54 cm, and then to find the number of packages divide the total number of centimeters of trim in the two packages, that is 858 cm by cetimeters of 90 inches, to simplify further as shown below:

  $\begin{array}{l}90\text{in}=90\times 2.54\\ =228.6\text{cm}\\ \text{858}÷\text{228}\text{.6}\\ \text{=3}\text{.75}\approx \text{4packages}\end{array}$

So, about 4 packages of 90 inches trim.