Answer:
<em>Herlene has 8 dimes and 17 quarters</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
x = number of dimes Herlene has
y = number of quarters Herlene has
Since each dime has a value of $0.10 and each quarter has a value of $0.25, the total money Herlene has is 0.10x+0.25y.
We know this amount is $5.05, thus:
0.10x + 0.25y = 5.05 [1]
It's also given the number of quarters is one more than twice the number of dimes, i.e.:
y = 2x + 1 [2]
Substituting in [1]:
0.10x + 0.25(2x + 1) = 5.05
Operating:
0.10x + 0.5x + 0.25 = 5.05
0.6x = 5.05 - 0.25
0.6x = 4.8
x = 8
From [2]:
y = 2*8 + 1 = 17
y = 17
Herlene has 8 dimes and 17 quarters
Answer: x1 = 251/26, x2 = -111/26
Step-by-step explanation:
Hi!
As you can see in the figure, the point you are looking for is the intersection of two lines.
The intersection point is found solving this system of linear equations (the point must satisfy both equations):

You can solve it, for example, by the method of substitution:

Then plug x1 into equation 2, and solve for x2:

Then you use the value of x2 to get x1:

Daniel because 3/4 is larger than 5/12 if you cross multiply.