Reduce the equation 30.7t−14.7=11.3t+32.930.7𝑡−14.7=11.3𝑡+32.9 to the form mt+b=0𝑚𝑡+𝑏=0 and solve it. Write down the answer as a decimal. Round off to two decimal places.
Question
Reduce the equation 30.7t−14.7=11.3t+32.930.7𝑡−14.7=11.3𝑡+32.9 to the form mt+b=0𝑚𝑡+𝑏=0 and solve it. Write down the answer as a decimal. Round off to two decimal places.
Solution
First, let's simplify the equation by subtracting 11.3t from both sides:
30.7t - 11.3t = 11.3t + 32.9 - 11.3t
This simplifies to:
19.4t - 14.7 = 32.9
Next, let's get the equation into the form mt + b = 0 by subtracting 32.9 from both sides:
19.4t - 14.7 - 32.9 = 0
This simplifies to:
19.4t - 47.6 = 0
Now, let's solve for t by adding 47.6 to both sides and then dividing by 19.4:
(19.4t - 47.6 + 47.6) / 19.4 = 47.6 / 19.4
This simplifies to:
t = 47.6 / 19.4
Using a calculator, we find that t = 2.45 when rounded to two decimal places.
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