Boris is ordering supplies for his company. He ordered 25 boxes of pencils and 40 boxes of pens. What is the ratio of boxes of pens ordered to boxes of pencils ordered?

8:5

Step-by-step explanation:

40:25 can be simplified by diving by 5. You get 8:5 for the ratio of the number of boxes of pens to the number of boxes of pencils, and the ratio cannot be reduced any more from here.

1. You must apply the Secant and Tangent segment theorem, which establishes:

 Tangent²=(The whole secant segment)(External secant segment)

 2. The whole secant segment is: AD=a+12

 3. The external secant segment is: BD=10

 4. The tangent segment is: DE=12

 5. Then, you have:

 DE²=ADxBD
 12²=(a+10)10
 10(a+10)=12²

 6. Therefore, the answer is the third option: 10(a+10)=12²