Jill gets 1.5 her hourly rate after she works 40 hours. She worked 52 hours and earned 638. What is her hourly rate?
I ALWAYS get a repeating decimal! I need help!
40x- 12(1.5x)= 638
26.66...-12x= 638
Now what do I do? It's a repeating decimal!
40 r + 12 (1.5 r) = 638
(why did you subtract, she earns more for those 12 hours)
58 r = 638
r = 11
To solve the equation 26.66...-12x=638, we need to handle the repeating decimal. One approach is to convert the repeating decimal into a fraction. Let's call the repeating decimal y, then we have:
y = 26.666...
To eliminate the repeating decimal, multiply both sides of the equation by 10 to get:
10y = 266.666...
Now, subtract the original equation from the new one:
10y - y = 266.666... - 26.666...
Simplifying the right side, we have:
9y = 240
Divide both sides of the equation by 9 to solve for y:
y = 240 / 9
y = 26.666...
Thus, the repeating decimal 26.666... can be expressed as a fraction 240/9.
Now, substitute this fraction back into the equation:
240/9 - 12x = 638
Simplify the equation:
240 - 108x = 638
Next, isolate the x term by subtracting 240 from both sides:
-108x = 398
Finally, divide both sides of the equation by -108 to solve for x:
x = 398 / -108
Simplify the fraction:
x = -3.685
Therefore, Jill's hourly rate is approximately -3.685. However, since hourly rates cannot be negative, there might be a mistake in the calculations. I would recommend rechecking the equation to ensure correctness.