APPLICATION OF TRANSLATING WORD PHRASES
You know how to evaluate algebraic expressions and how to translate word sentences. These two skills are used when finding solutions to "word problems”. First, you need to interpret the information into an algebraic expression. Then, you may use the given values to find the solution.
Definition: A formula is a concise, condensed set of math instructions in equation form.
When creating formulas, you want to choose variables that associate with the given information. For example, if your formula uses the length of a side, then use the letter L to represent the length in your formula.
EXAMPLES:
1) a) Write a formula for the perimeter of a rectangle.
The perimeter (P) of any figure is the sum of all its sides. We know a rectangle has four sides in which the opposite sides are equal. Therefore, two opposite sides will be called the lengths (L) and the other two opposite sides will be called the width (W).
P = L + L + W + W
P = 2L + 2W (combine like terms)
b) Find the perimeter of the rectangles with the following dimensions; length is
3 cm and width is 12 cm.
P = 2(3) + 2(12)
P = 6 + 24
P = 30 cm (include units in final answer)
see more examples below
2) Write a formula for the cost of a taxi ride if a certain taxi company charges a $2.00 flat fee plus 25 cents per mile.
Sometimes it proves helpful to try a few numerical examples first and then create the formula once you notice a pattern. For example, find the cost of a taxi ride that travels 5 miles, 15 miles and 33 miles.
for 5 miles: 0.25(5) + 2.00
for 15 miles: 0.25(15) + 2.00
for 33 miles: 0.25(33) + 2.00
When creating the formula decide what your variable should represent (what value changes, what is the unknown). For this example the variable will represent the number of miles.
When writing your answer, always state what the variable represents.
Let m = the number of miles and C = the total cost of taxi ride
The formula is C = 0.25m + 2.00
(Each value of money should be expressed as dollars and cents or just cents. For example, if you wrote the formula as such, 25m + 2, you would be incorrect because the 25 would be understood as $25 not 25 cents.)
3) A certain travel agent earns $6.00 per hour plus 0.5% commission on each transaction. Write a formula for her weekly pay. (Assume a 40 hour work week.)
Since we know the exact number of hours the travel agent works we can calculate her hourly pay. 6(40) = $240.00
The unknown information is how many transactions the travel agent will conduct. Therefore, let t = amount of transactions and let W = total weekly pay.
Note: In a formula or equation, percents should be converted to a decimal.
The formula is W = 240 + 0.005t
4) A phone company charges $3.50 for the first three minutes of a phone call and $0.30 for each additional minute. Write a formula for the cost of a phone call.
The unknown information is the number of minutes of the phone call.
Therefore, let m = the number of minutes of the phone call and let C = total cost.
The formula is C = 3.50 + 0.30(m - 3)
Note: If a phone call is 40 minutes, the first 3 minutes are accounted for in the flat fee of $3.50. Therefore, you would pay $0.30 for the additional 37 (40 - 3) minutes.
EXAMPLES:
Use the appropriate formula found above to calculate the following information.
1) Calculate the total cost of a phone call that lasted 2 hours and 20 minutes.
Use the formula C = 3.50 + 0.30(m - 3) where m = 140 minutes (need to convert hours to minutes).
Now substitute the value: C = 3.50 + 0.30(140 - 3)
3.50 + 0.30(137)
3.50 + 41.10
C = $44.60
2) Calculate the total cost of a taxi ride from NewarkLibertyAirport to BloomfieldCollege if the distance is 17 miles.
Use the formula C = 0.25m + 2.00 where m = 17 miles.
Now substitute the value: C = 0.25(17) + 2.00
C = 4.25 + 2.00
C = $6.25
3) Calculate the total weekly pay of a travel agent if she works a 40 hour week and made $14000 in transactions.
Use the formula W = 240 + 0.005t where t = $14000 in transactions.
Now substitute the value: W = 240 + 0.005(14000)
W = 240 + 70
W = $310