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

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.