Question

# The value of x for the provided equation displaystyle{0.12}{x}+{0.14}{left({550}-{x}right)}={72.5} and express the solution in decimal form, and also check the solution to the equation.

Decimals
The value of x for the provided equation $$\displaystyle{0.12}{x}+{0.14}{\left({550}-{x}\right)}={72.5}$$ and express the solution in decimal form, and also check the solution to the equation.

2021-02-21
Approach:
To solve an equation with decimal places, there are two commonly used procedures. One of the procedures is to store numbers in decimal form, then solve the equation by applying properties. Next procedure is to multiply both sides of the equation by an appropriate power of 10 clear the equation of all decimals.
Calculation:
Since, keep this equation in decimal form.
Consider, $$\displaystyle{0.12}{x}+{0.14}{\left({550}-{x}\right)}={72.5}$$
$$\displaystyle{0.12}{x}+{77}-{0.14}{x}={72.5},$$ apply distributive property.
$$\displaystyle-{0.02}{x}={72.5}-{77},$$ add like terms.
$$\displaystyle-{0.02}{x}=-{4.5}$$
$$\displaystyle{x}=\frac{4.5}{{0.02}}$$
$$\displaystyle={225}$$
Check the solution by putting the value of x in the provided equation.
$$\displaystyle{0.12}{x}+{0.14}{\left({550}-{x}\right)}={72.5}$$
$$\displaystyle{0.12}{\left({225}\right)}+{0.14}{\left({550}-{225}\right)}={72.5}$$
$$\displaystyle{27}+{77}-{31.5}={72.5}$$
$$\displaystyle{72.5}={72.5}$$
Answer: The solution set is 225.