Section 2-9
Problem Solving Using Linear Models
Many word problems can be translated into linear equations, and then solved
using the techniques discussed in this chapter.
You need to figure out which operations are being used, and what the unknowns
are.
Example:
You're shopping for a class camping trip. Suppose you have $60.00 to spend
on trail mix and dried fruit. Trail mix costs $3.00 per pound, and dried
fruit costs $5.00 per pound. Write an equation in standard form that represents
the different amounts (in pounds) of trail mix, T, and dried fruit, D,
you could buy.
If you buy 5 pounds of trail mix, how many pounds of trail mix can you
buy?
The standard-form equation is:
3T + 5D = 60
Substitute T = 5.
3(5) + 5D = 60
5D = 45
D = 9
So, if you buy 5 pounds of trail mix, you have money left to buy 9 pounds of
dried fruit.