Question

At the beginning of the year, Sadie had $70 in savings and saved an additional $18 each week thereafter. Jack started the year with $90 and saved $14 every week. Let S S represent the amount of money Sadie has saved t t weeks after the beginning of the year and let J J represent the amount of money Jack has saved t t weeks after the beginning of the year. Write an equation for each situation, in terms of t , t, and determine the amount of money Sadie and Jack have saved in the week that they have the same amount of money saved.

Answer 1

$160

Explanation:

Step one:

For Sadie

initial savings balance= $70

weekly savings = $18

Let S represent the amount of money Sadie has saved

and t the number of weeks after the beginning of the year

The total amount in savings after t weeks is

S=18t+70-------1

For Jack

initial savings balance= $90

weekly savings = $14

Let J represent the amount of money Jack has saved

and t the number of weeks after the beginning of the year

The total amount in savings after t weeks is

J=14t+90---------2

Step two

equation 1 and 2 to find t

18t+70=14t+90

18t-14t=90-70

4t=20

divide both sides by 4

t=20/4

t=5 weeks

so after 5 weeks Sadie and Jack will have the same amount of money

For Sadle t=5

S=18(5)+70-------1

S=90+70

S=$160

For Jack t=5

J=14(5)+90---------2

J=70+90

J=160

The two equations above shows that after 5 weeks their savings will be $160