Chapter 6.1, Problem 39PPE

To determine

Tofind:The system of equations that gives the amount in each over the time usingthe balance ( b ) −time ( t ) graphs of two accounts, and find the time when two bank accounts will have same balance.

Answer to Problem 39PPE

The balance-time equation of accounts 1 and 2 are $b=2.5t+40$ and $b=5t$ respectively.

Two bank accounts will have same balance at 16^th week.

Explanation of Solution

Given information:

The graphs showing balance b in dollars, and time t (in weeks) of two accounts are given in Fihure-1 here.

Formulaused:

The equation of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ .

Calculations:

The b - t graph of account 1 passes through points $\left(0,40\right)$ and $\left(4,50\right)$

The equation of account 1 is $b-40=\frac{50-40}{4-0}\left(t-0\right)$

  $\Rightarrow b-40=\frac{10}{4}t$

  $\Rightarrow b=2.5t+40$

The b - t graph of account 2 passes through points $\left(0,0\right)$ and $\left(4,20\right)$

The equation of account 1 is $b-0=\frac{20-0}{4-0}\left(t-0\right)$

  $\Rightarrow b=\frac{20}{4}t$

  $\Rightarrow b=5t$

Now, two bank accounts will have same balance at 16^th week when

  $2.5t+40=5t$

  $\Rightarrow t=\frac{-40}{-2.5}=16\text{weeks}$

Thus, when two bank accounts will have same balance at 16^th week.

Conclusion:

The balance-time equation of accounts 1 and 2 are $b=2.5t+40$ and $b=5t$ respectively.

Two bank accounts will have same balance at 16^th week.