Question

Brock is training for a Crossfit competition. He began the training by completing pull-ups and box jumps. Originally, his training plan had him completing pull-ups and box jumps at a ratio of 5:4. After two months of training, he decided to focus on his leg strength and adjusted his ratio to 2:7. If he completed 53 box jumps at the end of his training, how many pull-ups did he complete in the initial stage of training?

Answer 1

Answer:

Brock completed approximately 38 pull ups in the initial stage of training.        

Step-by-step explanation:

We are given the following information in the question:

Ration of pull ups and box jumps initially =

$\displaystyle\frac{5}{4}$  

Ration of pull ups and box jumps later =

$\displaystyle\frac{2}{7}$    

Number of box jumps completed in the end of training = 53

Total number of exercises done in the end = 2x + 7x = 9x

We use the concept of ratio.

$7x = 53\\\\=x = \displaystyle\frac{53}{7}\\\\\Rightarrow 2x = \frac{106}{7}\\\\\Rightarrow \text{Total number of excercise} = \frac{477}{7}$

Initially,

Total number of exercise = 5y + 4y

$9y = \displaystyle\frac{477}{7}\\\\\Rightarrow y = \frac{477}{63}\\\\\Rightarrow \text{Pull ups done initially} = 5y = 5\times \frac{477}{63} = 37.85 \approx 38$

Thus, he completed approximately 38 pull ups in the initial stage of training.