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Word Problem Exercises: Applications of 3 Equations with 3 Variables

Unless it is given, translate the problem into a system of 3 equations using 3 variables.
Solve the system and answer the question.

General Questions

Marina had $24,500 to invest.  She divided the money into three different accounts. At the end of the year, she had made $1,300 in interest.  The annual yield on each of the three accounts was 4%, 5.5%, and 6%.  If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had she placed in each account?

The currents running through an electrical system are given by the following system of equations.  The three currents, I1, I2, and I3, are measured in amps.  Solve the system to find the currents in this circuit.
I1 + 2I2 - I3 = 0.425
3I1 - I2 + 2I3 = 2.225
5I1 + I2 + 2I3 = 3.775

Find the equation of the parabola,y = ax2 + bx + c, that passes through the following three points:
(-2, 40), (1, 7), (3, 15).

Billy’s Restaurant ordered 200 flowers for Mother’s Day.  They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each.  They ordered mostly carnations, and 20 fewer roses than daisies.  The total order came to $589.50.  How many of each type of flower was ordered?

The Arcadium arcade in Lynchburg, Tennessee uses 3 different colored tokens for their game machines.  For $20 you can purchase any of the following mixtures of tokens:  14 gold, 20 silver, and 24 bronze; OR, 20 gold, 15 silver, and 19 bronze; OR, 30 gold, 5 silver, and 13 bronze.  What is the monetary value of each token?

In the position function for vertical height, s(t) = ½at2 + v0t + s0, s(t)represents height in meters and t represents time in seconds.

(a) Find the position function for a volleyball served at an initial height of one meter, with height of 6.275 meters ½ second after serve, and height of 9.1 meters one second after serve.
(b) How long until the ball hits the ground on the other side of the net if everyone on that team completely misses it?

Last Tuesday, Regal Cinemas sold a total of 8500 movie tickets.  Proceeds totaled $64,600.  Tickets can be bought in one of 3 ways:  a matinee admission costs $5, student admission is $6 all day, and regular admissions are $8.50.  How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?

K Dodd

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