Solve Equations with Decimal Coefficients In the following exercises, solve the equation 0.10d+0.25(d+5)=4.05

DofotheroU 2021-08-03 Answered
Solve Equations with Decimal Coefficients In the following exercises, solve the equation by clearing the decimals.
\(\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}\)

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Expert Answer

opsadnojD
Answered 2021-08-04 Author has 19932 answers
Step 1
The given equation is \(\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}\)
The equation \(\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}\) can be solved as follows.
Wemultiply the decimal number by 100 to shift the decimal towards right hand side by two place.
Step 2
For clearing the decimals we multiply each term by 100.
\(\displaystyle\Rightarrow{100}\times{0.10}{d}+{100}\times{0.25}{\left({d}+{5}\right)}={100}\times{4.05}\)
\(\displaystyle\Rightarrow{10}{d}+{25}{\left({d}+{5}\right)}={405}\)
\(\displaystyle\Rightarrow{10}{d}+{25}{d}+{125}={405}\)
Subtract 125 on sides.
\(\displaystyle\Rightarrow{10}{d}+{25}{d}+{125}-{125}={405}-{125}\)
\(\displaystyle\Rightarrow{35}{d}={280}\)
Divide both sides by 35.
\(\displaystyle\Rightarrow{\frac{{{35}{d}}}{{{35}}}}={\frac{{{280}}}{{{35}}}}\)
\(\displaystyle\Rightarrow\ {d}={8}\)
Therefore, \(\displaystyle{d}={8}\) is the solution of \(\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}.\)
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