Question

The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it?

10 weeks

13 weeks

15 weeks

21 weeks

Answer 1

13 weeks.

Our equation is
`y=-24x + 379`.
x is the amount of weeks that has passed. x is being multiplied by -24. The +379 is our y-intercept. This means that per week, the account loses $24. The y-intercept also means that the account started with having $379 in it.

Finally, y is the output of the equation. This means that when you plug in the number of weeks, we see how much money is in the bank account with the y-value.

For example, if we solve for 2 weeks;

`y=-24(2)+379=-48+379=331`. So after 2 weeks, the account will have $331 left.

Now to find the answer. We can plug in the final amount that we are given ($67) and then solve from there.

`67=-24x+379`

Next we isolate x and its coefficient:

`67-379=-24x+379-379`

`-312=-24x`

Multiply both by -1 to get positive numbers:

`-312*-1=-24x*-1`

`312=24x`

Now divide both sides by 24 to completely isolate x.

`(312)/(24)=(24x)/(24)`

`13=x`

OR

`x=13`.

This means that when x = 13, y = 67. When 13 weeks pass, the amount of money in the account is equal to $67.

Therefore, the amount of time it takes for the account to be depleted to $67 is 13 weeks.