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
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:
Step-by-step explanation:
The equation for the first ratios would be:
\(\frac{L}{P}=\frac{1}{5}\)
Where \(L\) is Lela's points, and \(P\) is Pepe's points.
Then, the problem states that there were added bonus points to Lela. So, the new points would be \(L+48\) with a new ratio \(5:9\). The second proportion would be:
\(\frac{L+48}{P}=\frac{5}{9}\)
Now, we solve these two equation as a system, to find Lela's score:
\(\frac{L}{P}=\frac{1}{5}\\P=5L\)
Then, we replace this in the second equation:
\(\frac{L+48}{P}=\frac{5}{9}\\\frac{L+48}{5L}=\frac{5}{9}\\9L+432=25L\\432=25L-9L\\432=16L\\L=\frac{432}{16}=27\)
Therefore, Lela's score is 27+48=75.