If owen has a collection of nickels and quarters worth $8.10. if the nickles were quarters and the quarters were nickels, the value would be 17.70 find the number of each coin?

Answer with Step-by-step explanation:

Let there be n nickle and q quarters

Owen has a collection of nickels and quarters worth $8.10.

i.e. 0.05n+0.25q=8.10

Multiplying both sides by 20

n+5q=162        (1)

if the nickles were quarters and the quarters were nickels, the value would be $17.70

i.e. 0.05q+0.25n=17.70

Multiplying both sides by 20

q+5n=354       (2)

equation (1)×5-(2), we get

5n+25q-(q+5n)=810-354

24q=456

dividing both sides by 24,we get

q=19

Putting q=19 in (2),we get

19+5n=354

Subtract both sides by 19,we get

5n=335

Dividing both sides by 5, we get

n=67

Hence, Number of nickle=67

Number of quarter=19

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.