This week in Math 10, I have chosen to talk about linear equation systems in word problems.

When it comes to linear equations, word problems can be quite simple to rather complex, like these two examples.

“The sum of two numbers is 42. The larger number is two times the smaller number. Find the numbers.”

“A jet airliner moving against 79 km/h wind at 903 km/h arrives at an airport after 6 hours. On the return trip, it takes 5 hours with the wind to reach the origin airport. Determine the distance between the airports.”

Interpreting the word problems requires you to keep an eye out for terms that indicate values. Taking the first example…

“The sum of two numbers is 42. The larger number is two times the smaller number. Find the numbers.”

To begin, declare variables with the following statement.

Let x=larger number
y=smaller number

While changing variable names and representations when needed.

For the more complex problems like the second example, you can use a table to help you create the system. First, we read the problem.

“A jet airliner moving against 79 km/h wind at 903 km/h arrives at an airport 5652 km away. On the return trip, it travels with the same wind to reach the origin airport. Determine the time for both trips.”

Now, we put this information into a 9×9 table, like so.

x	903-79	5652
y	903+79	5652

In this table, each column represents, from left to right, time, speed and distance. In this case, the bottom row is unused; it would have been used for a total, if applicable. Another problem that has this total would be the following.

“A chemist is mixing 500 mL of E85 ethanol fuel (85% ethanol) from bottles of 40% ethanol and 95% ethanol solutions. Determine how much 40% ethanol was used.”

In this case, from left to right, the columns represent amount, rate and value. (Or mL, % of ethanol, mL of ethanol.) Let x=40% ethanol and y=95% ethanol.

x	40% (0.4)	0.4x
y	95% (0.95)	0.95y
500	85% (0.85)	0.85(500)=425