Exercise 73 Page 262

To be able to use algebra, let's introduce variables.

Let's use these variables to write equations representing the information given in the question.

Information	Equation
Yoko bought $10$ traveller's checks.	$t + f + h = 10$
The total value of the traveller's checks is $$ 370 .$	$20 t + 50 f + 100 h = 370$
Yoko bought twice as many $$ 20$ checks as $$ 50$ checks.	$t = 2 f$

We have three equations for three unknowns. Now we will solve this equation system. As a first step, let's substitute

t = 2 f

in the first two equations to eliminate the variable

t .

{t + f + h = 10 20 t + 50 f + 100 h = 370 (I) (II)

$t = 2 f$

{2 f + f + h = 10 20 (2 f) + 50 f + 100 h = 370

$(II):$ Multiply

{2 f + f + h = 10 40 f + 50 f + 100 h = 370

$(I), (II):$ Add terms

{3 f + h = 10 90 f + 100 h = 370

We will use the Elimination Method to solve this system of equations.

{3 f + h = 10 90 f + 100 h = 370 (I) (II)

$(II):$ $LHS / 10 = RHS / 10$

{3 f + h = 10 9 f + 10 h = 37

$(I):$ $LHS \cdot 3 = RHS \cdot 3$

{9 f + 3 h = 30 9 f + 10 h = 37

$(II):$ Subtract $(I)$

{9 f + 3 h = 30 9 f + 10 h - (9 f + 3 h) = 37 - 30

▼

(II):

Solve for

h

$(II):$ Distribute $- 1$

{9 f + 3 h = 30 9 f + 10 h - 9 f - 3 h = 37 - 30

$(II):$ Subtract terms

{9 f + 3 h = 30 7 h = 7

$(II):$ $LHS / 7 = RHS / 7$

{9 f + 3 h = 30 h = 1

$(I):$ $h = 1$

{9 f + 3 (1) = 30 h = 1

▼

(I):

Solve for

f

$(I):$ Multiply

{9 f + 3 = 30 h = 1

$(I):$ $LHS - 3 = RHS - 3$

{9 f = 27 h = 1

$(I):$ $LHS / 9 = RHS / 9$

{f = 3 h = 1

Since we know that

t = 2 f,

this result also implies that

t = 2 (3) = 6 .

Let's summarize how many of each type of traveler's check Yoko has.