Type the correct answer in each box. Use numerals instead of words.

Question

Theo and Kade worked on a school project together. Theo worked on the project 3 fewer hours than Kade did. Altogether, they worked for a total of 27 hours. How many hours did they each work on the school project?


Theo worked on the project for
______hours.
Kade worked on the project for
_____hours.

Answer 1

Let Kade's hours be represented as \( x \). According to the problem, Theo worked 3 fewer hours than Kade, so Theo's hours can be represented as \( x - 3 \).

The total hours worked by both is 27 hours, which can be expressed with the equation:

\[ x + (x - 3) = 27 \]

Simplifying this equation:

\[ 2x - 3 = 27 \]

Adding 3 to both sides:

\[ 2x = 30 \]

Dividing both sides by 2:

\[ x = 15 \]

So, Kade worked for 15 hours. Now, we can find out how many hours Theo worked:

\[ x - 3 = 15 - 3 = 12 \]

Thus, Theo worked for 12 hours.

In summary:

Theo worked on the project for 12 hours.
Kade worked on the project for 15 hours.