Question

name

1. geometry the volume of a box v is given by the formula ( v=ell w h ), where ( ell ) is the length, ( w ) is

the width, and ( h ) is the height.
a. solve the formula for ( h ).
b. what is the height of a box with a volume of 50 cubic meters, length of 10 meters, and width
of 2 meters?
example 4

1. coffee shop consuelo is buying flavored coffee and plain coffee. the total amount of money

she spends on coffee is ( t=5.50 p+7 f ), where ( p ) represents the cost of a package of plain
coffee and ( f ) represents the cost of a package of flavored coffee.
a. if consuelo has ( $ 40 ) to spend on coffee, describe the constraints on the formula.
b. solve for ( f ).
c. if consuelo needs to buy 3 packages of plain coffee, what is the maximum number of packages
of flavored coffee she can buy?

1. shopping kimberly is ordering bath towels and washcloths for the inn where she works. the

total cost of the order is ( t=6 b+2 w ), where ( t ) is the total cost, ( b ) is the number of bath
towels, and ( w ) is the number of washcloths.
a. her budget is ( $ 85 ). describe the constraints.
b. solve for ( b ).
c. she needs to order at least 20 washcloths. how many bath towels can she order and stay
under budget?

Explanation:

Step1: Solve the formula \(V = \ell wh\) for \(h\)

Divide both sides of the equation \(V=\ell wh\) by \(\ell w\).

$$h=\frac{V}{\ell w}$$

Step2: Substitute \(V = 50\), \(\ell=10\), and \(w = 2\) into the formula for \(h\)

Substitute the given values into \(h=\frac{V}{\ell w}\).

$$h=\frac{50}{10\times2}$$

Step3: Simplify the expression

First, calculate \(10\times2 = 20\). Then, \(\frac{50}{20}=\frac{5}{2}=2.5\)

Answer:

a. \(h=\frac{V}{\ell w}\)
b. \(2.5\) meters