Question

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

Answer 1

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.