Intermediate Algebra (11th edition)

Brain Busters Extend the method of this section to solve each system. Express the solution

in the form 1 x, y, z, w 2.

SECTION 4.3 Applications of Systems of Linear Equations 233

Solve each problem. See Sections 2.3 and 2.4.

47.The perimeter of a triangle is 323 in. The shortest side measures five-sixths the length of

the longest side, and the medium side measures 17 in. less than the longest side. Find the

lengths of the sides of the triangle.

48.The sum of the three angles of a triangle is 180°. The largest angle is twice the measure

of the smallest, and the third angle measures 10° less than the largest. Find the measures

of the three angles.

49.The sum of three numbers is 16. The greatest number is times the least, while the mid-

dle number is four less than the greatest. Find the three numbers.

50.Witny Librun has a collection of pennies, dimes, and quarters. The number of dimes is

one less than twice the number of pennies. If there are 27 coins in all worth a total of

$4.20, how many of each denomination of coin is in the collection?

- 3

PREVIEW EXERCISES

43.

• x- y+ z+ 2 w= 8

x- 2 y+ 3 z+ w= 18

2 x+ y- z+ w= 3

x+ y+ z- w= 5 44.

• x+y- z+ w=- 6

x-y- z+ 3 w=- 2

x+y+ 2 z- w= 10

3 x+y- z+ 2 w= 9

45.

5 x+ 4 y- 5 z+ 2 w=- 7

• 2 x+ 3 y- 5 z+ w= 3

2 x+ 4 y+ z- w=- 7

3 x+ y- z+ w=- 3 46.

4 x+ y- 3 z+ w= 22

3 x+ 2 y+ z+ 2 w= 19

2 x+ 4 y+ 6 z- 3 w=- 3

x- 3 y+ 7 z+ w= 11

OBJECTIVES

Applications of Systems of Linear Equations

4.3

1 Solve geometry
problems by using
two variables.

2 Solve money
problems by using
two variables.

3 Solve mixture
problems by using
two variables.

4 Solve distance-rate-
time problems by
using two variables.

5 Solve problems with
three variables by
using a system of
three equations.

Although some problems with two unknowns can be solved by using just one vari-

able, it is often easier to use two variables and a system of equations. The following

problem, which can be solved with a system, appeared in a Hindu work that dates

back to about A.D. 850. (See Exercise 35.)

The mixed price of 9 citrons (a lemonlike fruit) and

7 fragrant wood apples is 107; again, the mixed price of

7 citrons and 9 fragrant wood apples is 101. O you arith-

metician, tell me quickly the price of a citron and the

price of a wood apple here, having distinctly separated

those prices well.

When solving an applied problem using two variables, it is a good idea to pick

letters that correspond to the descriptions of the unknown quantities. In the ex-

ample above, we could choose cto represent the number of citrons, and wto

represent the number of wood apples.

PROBLEM-SOLVING HINT