abie has $3.25 in quarters and dimes. she has 8 more dimes than quarters. how many quarters and dimes does she have?

Question

solve with substitution elimination and by graphing. all 3 ways

Answer 1

Let the number of quarters = Q and the number of dimes = D.

 

We know the following:

0.25Q+0.10D = 3.25

D-8=Q

 

Using substitution:

0.25(D-8)+0.10D = 3.25 --> 0.25D+0.10D-2 = 3.25 --> 0.35D = 5.25 --> D = 15; Q = D-8 = 15-8 = 7

 

Using elimination:

10[0.25Q + 0.10D = 3.25] = 2.5Q + D = 32.5

 

2.5Q + D = 32.5

+  Q  -  D = -8

--> 3.5Q = 24.5 --> Q = 7; D = Q + 8 = 15

 

To solve graphically we can plot Q on the y-axis and D on the x-axis. If we treat each of the known equations as lines, our solution occurs where the two lines cross:

--> Solve both equations for Q:

      0.25Q = 3.25 - 0.10D --> Q = 13 - 0.4D

      Q = D - 8

 

When graphed, the two lines cross where Q and D are equal in both equations. Since the two equations are now both equal to Q, we can set them equal to each other to solve for D:

--> 13 - 0.4D = D - 8 --> 21 = 1.4D --> D = 15; Q = 15 - 8 = 7