4.3 Solving Applications Using Systems of Equations
Solve Application Problems That Translate to a 2X2 System of Equations
1.
Select a variable to represent each unknown
2.
Write a system of equations
3.
Solve the system
Hint: First determine what equation(s) make sense to use and set up a table to fill in.
In Short, Word Problems
Many of these word problems could be solved using only one variable.
Examples:
[00] If the sum of two numbers is 16 and the difference is 4, you could let one value be x and the other be
16 – x rather than setting it up as: x + y = 16 x - y = 4
then solving it. x = 10, y = 6
[14] Pier 1 sells 2 sizes of pillar candles. The larger sells for $15, the smaller for $10. One day the
number of small candles sold four more than twice the number of larger ones, for a total of $845.
How many of each were sold? cost = number × unit cost small 10x x 10 large 15y y 15
10x + 15y = 845 x = 4 + 2y small = 50; large = 23
[26] Going upstream, it takes 2 hr to travel 36 mi in a boat. Downstream, the same distance takes 1.5 hr.
Find the speed of the boat and the current.
distance = rate × time upstream 2( b - c ) b - c 2 downstream 1.5( b + c ) b + c 1.5
2 ( b – c ) = 36
1.5 ( b + c ) = 36 boat - 21 mph, current – 3 mph
[30] How much of a 45% saline solution and a 30% saline solution must be mixed to produce 20 liters
of 39% saline solution?
salt = % salt × solution
45% .45x .45 x
30% .30y .30 y x + y = 20
.45x + .30y = .39(20)
12 L of 45%, 8 L of 30%