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26 August, 17:44

Miguel wants to buy a new stereo that costs $320. He has $40 in March, $80 in April, and $120 in May. If this pattern continues, in what month will he be able to buy the stereo

a. September

b. October

c. November

d. December

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  1. 26 August, 17:56
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    March, April, and May correspond to 3,4, and 5th months. Each month the amount of money he saves increases by $40, so this is a constant rate of change, or constant velocity, which means that this is a linear equation. Let y=the amount of money he has and x=the month number and model it with the line of form y=mx+b, where m=slope, or rate, and b=y-intercept ...

    y=40x+b, we know that he has $40 on the third month (February) so:

    40=40 (3) + b

    40=120+b

    -80=b so the equation is:

    y=40x-80 (note that the domain is x=[3, + oo) only for the function to have meaining)

    Now you want to know when he has $320 ...

    320=40x-80

    400=40x

    10=x

    So he will have $320 on the 10th month, which is October.
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