At the beginning of the year, Ian had $30 in savings and saved an additional $15 each week thereafter. Brayden started the year with $70 and saved $5 every week. Let II represent the amount of money Ian has saved tt weeks after the beginning of the year and let BB represent the amount of money Brayden has saved tt weeks after the beginning of the year. Graph each function and determine the amount of money Ian and Brayden have saved in the week that they have the same amount of money saved.

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facundo3141592 facundo3141592 · Answer 1 · 2021-08-11T17:42:43+02:00

A linear equation can be written as:

[tex]y = a*x + b[/tex]

Where a is the slope and b is the y-intercept.

Defining x as the number of weeks since the start of the year, we can write the linear equations I and B as:

[tex]B(x) =\$70 + \$5*x[/tex]

(initial amount plus the amount that he saves each week times the number of weeks)

Similarly, for Ian we have:

[tex]I(x) = \$30 + \$15*x[/tex]

The graph of these lines can be seen below, where the blue one is I(x) and the green one is B(x).

Now we want to determine how much they had when they had the same amount.

This means that we need to solve:

B(x) = I(x)

Replacing the equations we get:

[tex]\$70 + \$5*x = \$30 + \$15*x[/tex]

Now we can solve this for x:

[tex]\$70 - \$30 = \$15*x - \$5*x[/tex]

[tex]\$40 = \$10*x[/tex]

[tex]\$40/\$10 = x[/tex]

[tex]4 = x[/tex]

So they have the same amount of money in week 4, and each one of them has:

[tex]B(4) = I(4) = \$70 + \$5*4 = \$70 + \$20 = \$90[/tex]

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