Exercise 97 Page 617

To solve the exercise we will introduce a few variables.

x y = number of weeks = money in the account

We know that Morgan started with

$ 615

in his bank account and is saving

$ 25

per week. With this information, we can write an equation that describes the amount of money in Morgan's account each week.

y = 615 + 25 x

Kendall has

$ 975

in his account and spends

$ 15

every month. With this information, we can write a second equation that describes the amount of money in Kendall's account each week.

y = 975 - 15 x

If we combine these equations, we get a system of equation which we can solve by the Substitution Method.

{y = 615 + 25 x y = 975 - 15 x (I) (II)

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Solve by substitution

$(I):$ $y = 975 - 15 x$

{975 - 15 x = 615 + 25 x y = 975 - 15 x

$(I):$ $LHS - 975 = RHS - 975$

{- 15 x = 25 x - 360 y = 975 - 15 x

$(I):$ $LHS - 25 x = RHS - 25 x$

{- 40 x = - 360 y = 975 - 15 x

$(I):$ $LHS \cdot (- 1) = RHS \cdot (- 1)$

{40 x = 360 y = 975 - 15 x

$(I):$ $LHS / 40 = RHS / 40$

{x = 9 y = 975 - 15 x

After

9

weeks they have the same amount of money in their accounts. Note that we do not have to bother solving for

y,

as we were only asked when they have the same amount of money in their account. We do not need to figure out what that amount is.