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Sagot :
Solution:
Let's make,
mechanic #1's rate = x
mechanic #2's rate = y
Note that their rate is dollars per hour.
Now, mechanic #1 worked for 20 hours. Then, we get the following equation:
20x = money earned by mechanic #1
On the other hand, mechanic #2 worked for 15 hours. Then, we get the following equation:
15y = money earned by mechanic #2
together they charged a total of $2250. So the amount of money earned by both mechanics is:
20x + 15y = 2250 EQUATION 1
On the other hand, the sum of the two rates was:
x + y = 125 EQUATION 2
From the equation, if we solve for x, we get:
x = 125-y EQUATION 3
plug (125-y) in for "x" in equation 1 to get everything in terms of one variable:
20(125-y)+15y = 2250
this is equivalent to
2500-20y +15y = 2250
this is equivalent to
2500 -5y = 2250
this is equivalent to
-5y = 2250 -2500
this is equivalent to:
-5y = -250
or
5y = 250
solving for y, we get:
[tex]y\text{ =}\frac{250}{5}=50[/tex]now, replacing this into equation 3, we get:
x = 125-y = 125 - (50) = 75
so that, we can conclude that the correct answer is:
mechanic #1 charged 75 $/hr
mechanic #2 charged 50 $/hr
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