Ralph chase graduated from college with a dept of $20000. He had taken out two different kinds of loans : a government loan at 3.3% APR ( annual percentage rate, or interest after one year) and a private loan at 4.9% APR . If his total interest after one year was $804 , how much money did he borrow from each source ?

Ralph borrowed $11,000 from the government source and $9,000 from the private source.

Step-by-step explanation:

Let:

x = government loan

y = private loan

x + y = 20,000 (1)

x = 20,000 - y (2)

0.033x + 0.049y = 804 (3)

Substitute equation (2) into (3) for x, we have:

0.033(20,000 - y) + 0.049y = 804

660 - 0.033y + 0.049y = 804

0.016y = 804 - 660

0.016y = 144

y = 144 / 0.016 = $9,000

Substitute $9,000 for y in equation (2), we have:

x = 20,000 - 9,000 = $11,000

Therefore, Ralph borrowed $11,000 from the government source and $9,000 from the private source.

step-by-step explanation:

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.