Ramiro earns $20 per hour during the week and $30 per hour for overtime on the weekends. One week Ramiro earned a total of $650. He worked 5 times a many hours during the week as he did on the weekend.

Week=25 Hours

Weekend= 5 Hours

Step-by-step explanation:

So we need to use the info they gave us and create two equations. Firstly we know how much he gets paid per hour during the week (x) and how much he gets paid on the weekend (y).

$20x+$30y=$650

We get this because we know the combined rates he is paid times the hours should add up to the amount he earned.

The next equation will be made off of the information that he worked 5 times as many hours during the week as on the weekend. This tells us that we will take the weekend hours (y) and multiply them by 5 in order to get the week hours (x).

x=5y      Now, since we have one variable by itself, we can plug it in for x in the first equation.

20(5y)+30y=650    Our first step here is to distribute the 20 to the 5y in order to eliminate the parenthesis.

100y+30y=650    Next add the like terms together (100y+30y).

Now all we have to do to find y is divide by 130 on both sides to get y alone.

130y=650  

130     130

y=5             Now to solve for x we just plug our y value into one of the equations above. I'm going to use the second equation.

x=5(5)

x=25      

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

5+2x=a

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