Problem 9
Translate each statement into an equation and then solve the equation for the
unknown number.
642 is the product of 6 and an unknown number.
Problem 9
Annual depreciation equals the difference between the original cost of an item
and its remaining value, divided by its estimated life in years. Determine the
annual depreciation of a new car that costs 25,000 dollar has an estimated
life of 10 years, and has a remaining value of 2000 dollar.
Problem 10
Translate each statement into an equation and then solve the equation for the
unknown number.
The sum of an unknown number and itself is 784.
Problem 10
Use the given formulas to determine the results.
In general, temperature is measured using either the Celsius (C) or Fahrenheit
(F) scales. To convert from degrees Celsius to degrees Fahrenheit, use the
following formula.
$$F=(9 C \div 5)+32$$
a. Use the formula to convert \(20^{\circ}\) Celsius into degrees Fahrenheit.
b. \(100^{\circ} \mathrm{C}\) is equal to how many degrees Fahrenheit?
Problem 11
To convert from degrees Fahrenheit to degrees Celsius, use the following
formula.
$$C=5(F-32) \div 9$$
a. Convert \(86^{\circ} \mathrm{F}\) into degrees Celsius.
b. What is a temperature of \(41^{\circ} \mathrm{F}\) equal to in degrees
Celsius?
Problem 11
In Exercises 11–17, solve each problem by applying the four steps of problem
solving. Use the strategy of solving an algebraic equation for each problem.
In preparing for a family trip, your assignment is to make the travel
arrangements. You can rent a car for \(\$ 75\) per day with unlimited mileage.
If you have budgeted \(\$ 600\) for car rental, how many days can you drive?
Problem 12
The distance an object travels is determined by how fast it goes and for how
long it moves. If an object's speed remains constant, the formula is \(d=r t,\)
where \(d\) is the distance, \(r\) is the speed, and \(t\) is the time.
a. If you drive at 50 miles per hour for 5 hours, how far will you have
traveled?
b. A satellite is orbiting Earth at the rate of 250 kilometers per minute. How
far will it travel in 2 hours?
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Problem 12
Solve each problem by applying the four steps of problem solving. Use the
strategy of solving an algebraic equation for each problem.
You need to drive 440 miles to get to your best friend’s wedding. How fast
must you drive to
get there in 8 hours?
Problem 13
Solve each problem by applying the four steps of problem solving. Use the
strategy of solving an algebraic equation for each problem.
Your goal is to save \(\$ 1200\) to pay for next year's books and fees. How much
must you save each month if you have 5 months to accomplish your goal?
Problem 13
Translate the following verbal rules into symbolic rules using \(x\) as the
input and \(y\) as the output variable.
a. The output is ten more than the input.
b. The output is the sum of the input and 12
c. The output is five less than the input.
d. The output is six times the input.
e. The output is three less than six times the input.
f. The output is six times the difference of the input and three.
g. The output is 25 less than the input squared.
