Jessica, Lena, and Rory scored all the soccer team's 43 goals this past season. Lena scored three times as many goals as Jessica, and Rory scored 2 fewer goals than Jessica. How many goals did Rory score?

Total goals: 43

Equation:

Let [tex]\( J \)[/tex] be the number of goals scored by Jessica.
Let [tex]\( L \)[/tex] be the number of goals scored by Lena.
Let [tex]\( R \)[/tex] be the number of goals scored by Rory.

[tex]\[ L = 3J \][/tex]
[tex]\[ R = J - 2 \][/tex]
[tex]\[ J + L + R = 43 \][/tex]

How many goals did Rory score?



Answer :

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.