Alright, let's break this problem down step-by-step to find out how many goals Rory scored.
1. Define Variables:
- Let [tex]\( J \)[/tex] be the number of goals scored by Jessica.
- Lena scored three times as many goals as Jessica, so she scored [tex]\( 3J \)[/tex] goals.
- Rory scored 2 fewer goals than Jessica, which means Rory scored [tex]\( J - 2 \)[/tex] goals.
2. Set Up the Equation:
- The total number of goals scored by Jessica, Lena, and Rory is 43. Therefore, we can write the equation:
[tex]\[
J + 3J + (J - 2) = 43
\][/tex]
3. Combine Like Terms:
- Combine all the [tex]\( J \)[/tex] terms and simplify the equation:
[tex]\[
J + 3J + J - 2 = 43
\][/tex]
[tex]\[
5J - 2 = 43
\][/tex]
4. Solve for [tex]\( J \)[/tex]:
- Add 2 to both sides of the equation to isolate the term with [tex]\( J \)[/tex]:
[tex]\[
5J - 2 + 2 = 43 + 2
\][/tex]
[tex]\[
5J = 45
\][/tex]
- Divide both sides by 5 to solve for [tex]\( J \)[/tex]:
[tex]\[
J = \frac{45}{5}
\][/tex]
[tex]\[
J = 9
\][/tex]
- So, Jessica scored [tex]\( 9 \)[/tex] goals.
5. Calculate Rory's Goals:
- Rory scored 2 fewer goals than Jessica. Since Jessica scored 9 goals, Rory scored:
[tex]\[
9 - 2 = 7
\][/tex]
Therefore, Rory scored 7 goals.
