Lela and pepe are playing a video game. The ratio of Lela's game score to pepe score is 1:5. Lela completes a quest and gain 48 bonus points. Their ratio is now 5:9. What is lela's score



Answer :

Before the bonus points were added their scores were as follow
Pepe: 135
Lela: 27
And with the addition of those 48 points her new score is 75 points

Answer:

75

Step-by-step explanation:

The equation for the first ratios would be:

[tex]\frac{L}{P}=\frac{1}{5}[/tex]

Where [tex]L[/tex] is Lela's points, and [tex]P[/tex] is Pepe's points.

Then, the problem states that there were added bonus points to Lela. So, the new points would be [tex]L+48[/tex] with a new ratio [tex]5:9[/tex]. The second proportion would be:

[tex]\frac{L+48}{P}=\frac{5}{9}[/tex]

Now, we solve these two equation as a system, to find Lela's score:

[tex]\frac{L}{P}=\frac{1}{5}\\P=5L[/tex]

Then, we replace this in the second equation:

[tex]\frac{L+48}{P}=\frac{5}{9}\\\frac{L+48}{5L}=\frac{5}{9}\\9L+432=25L\\432=25L-9L\\432=16L\\L=\frac{432}{16}=27[/tex]

Therefore, Lela's score is 27+48=75.