Word problems that lead to Section 2 Problem 1. A woman is now 30 years older than her son. 15 years ago, she was twice as old. What are the present ages of the woman and her son? To see the answer, pass your mouse over the colored area. Let Let Here are the equations:
To eliminate You should find: Therefore Problem 2. A total of 925 tickets were sold for $5,925. If adult tickets cost $7.50, and children's tickets cost $3.00, how many tickets of each kind were sold? (Compare Example 2.) Let Here are the equations:
In equation 2), make the coefficients into whole numbers by multiplying both sides of the equation by 10:
To eliminate Multiply equation 1) by −30, and add. The solution is:
Problem 3. Mr. B. has $20,000 to invest. He invests part at 6%, the rest at 7%, and he earns $1,280 interest. How much did he invest at each rate? (Compare Example 3.) Let Here are the equations:
To eliminate Multiply equation 1) by −6, and add. The solution is:
Problem 4. Edgar has 20 dimes and nickels, which together total $1.40. How many of each does he have? (Compare the Problem in Section 1.) Let Here are the equations:
To eliminate The solution is:
Problem 5. How many gallons of 20% alcohol solution and how many of 50% alcohol solution must be mixed to produce 9 gallons of 30% alcohol solution? (Compare Example 4.) (9 gallons of 30% alcohol solution = .3 × 9 = 2.7 gallons of pure alcohol.) Let Here are the equations:
To eliminate The solution is:
Problem 6. 15 gallons of 16% disenfectant solution is to be made from 20% and 14% solutions. How much of those solutions should be used? (15 gallons of 16% solution = .16 × 15 = 2.4 gallons of pure disenfectant.) Let Here are the equations:
To eliminate The solution is:
Problem 7. It takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstream. What is the speed of the boat in still water, and how fast is the current? (Compare Example 6.) Let Here are the equations:
To eliminate The solution is:
Problem 8. An airplane covers a distance of 1500 miles in 3 hours
wind. What is the speed of the plane in still air? (Compare Example 6.) Let Here are the equations:
To eliminate The solution is:
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