Edward spent 2/15 of his savings to renovate his office and 1/3 of it to buy a car. If he spent $39000 more on the car than on the renovation of his office, how much savings did he have left?

1 answer

Let \( S \) be the total savings that Edward has.

Edward spent \( \frac{2}{15}S \) on renovating his office and \( \frac{1}{3}S \) on buying a car. The problem states that he spent $39,000 more on the car than on the renovations, which we can express mathematically as:

\[ \frac{1}{3}S = \frac{2}{15}S + 39000 \]

To solve for \( S \), we first convert \( \frac{1}{3}S \) to a fraction with a denominator of 15:

\[ \frac{1}{3}S = \frac{5}{15}S \]

Now we can rewrite the equation:

\[ \frac{5}{15}S = \frac{2}{15}S + 39000 \]

Next, we subtract \( \frac{2}{15}S \) from both sides:

\[ \frac{5}{15}S - \frac{2}{15}S = 39000 \]

This simplifies to:

\[ \frac{3}{15}S = 39000 \]

Which further simplifies to:

\[ \frac{1}{5}S = 39000 \]

To find \( S \), we multiply both sides by 5:

\[ S = 39000 \times 5 = 195000 \]

Now, we have Edward's total savings:

\[ S = 195000 \]

Next, we will calculate how much he spent on the renovations and the car:

  1. Renovation: \[ \frac{2}{15}S = \frac{2}{15} \times 195000 = 2 \times 13000 = 26000 \]

  2. Car: \[ \frac{1}{3}S = \frac{1}{3} \times 195000 = 65000 \]

To confirm that he spent \( 39000 \) more on the car than on the renovation:

\[ 65000 - 26000 = 39000 \]

Now, we can find his remaining savings after these expenditures:

\[ \text{Remaining Savings} = S - \left( \text{Amount spent on renovations} + \text{Amount spent on car} \right) \] \[ = 195000 - (26000 + 65000) \] \[ = 195000 - 91000 = 104000 \]

Thus, Edward has \(\boxed{104000}\) left in savings.