Answer:
Marry = $17
Ravi = $11
Alan = $34
Step-by-step explanation:
Let us assume
Mary be X
Ravi be Y
Alan be Z
So, the equation in total is
X + Y + Z = 62
It is given that
X = Y + 6
Z = 2X
Now we put the Z value in the total equation, so it would be
X + Y + 2X = 62
3X + Y = 62 .................................... (1)
And can we write
X = Y + 6
X - Y = 6 ................................. (2)
Now substitution these two equations,
3X + Y = 62
X - Y = 6
2X = 68
X = $17
So, Z = 2 × 17 = $34
And, Y
$17 + Y + $34 = $62
So, Y = $11
The student should have phrased it to be "the difference between the product of 5 and y and 15", as the way the student writes it implies that 5y is being subtracted from 15 instead of the other way around.
You have two unknown rates, so we need to develop two equations to solve for these unknowns (based on the information given on the problem statement):
5x + 10y = 725
x + y = 100
By substitution, we get:
5x + 10(100 - x) = 725
5x + 1000 - 10x = 725
-5x = 725 - 1000
-5x = -275
x = -275/-5 = 55
100 - 55 = 45
Thus:
The mechanic who worked for 5 hours charged his time at $55/hr, and the mechanic who worked for 10 hours charged his time at $45/hr.
To verify, plug and chug the results back into the original equations:
5(55) + 10(45) = 725
275 + 450 = 725
725 = 725 [OK]
55 + 45 = 100 [OK]