Question

# Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cos

Modeling
Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost $175. The mechanic charges$34 per hour. If you receive an estimate for at least $226 and at most$294 for fixing the car, what is the time interval that the mechanic will be working on the job?

2021-05-19

Let's note: x=the time interval that the mechanic will be working on the job
We write the inequalities modeling the problem: $$\displaystyle{226}\le{175}+{34}{x}\le{294}$$
We solve the inequalities: $$\displaystyle{226}-{175}\le{175}+{34}{x}-{175}\le{294}-{175}$$
$$\displaystyle{51}\le{34}{x}\le{119}$$
$$\displaystyle\frac{{51}}{{34}}\le\frac{{110}}{{34}}$$
$$\displaystyle{1.5}\le{x}\le{3.5}$$