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Jimmy is a tutor in the science club. He charges [tex][tex]$\$[/tex]40[tex]$[/tex] per semester to privately tutor other students and an additional [tex]$[/tex]\[tex]$10$[/tex][/tex] for home visits to help him pay for gas. If Jimmy made less than [tex][tex]$\$[/tex]80$[/tex] this semester for tutoring 1 student, which inequality can be used to determine how many times he visited the student's home?

A. [tex]50x \ \textless \ 80[/tex]
B. [tex]40 + 10x \ \textless \ 80[/tex]
C. [tex]\frac{x}{10} + 40 \ \textless \ 80[/tex]
D. [tex]40x + 10 \ \textless \ 80[/tex]

Sagot :

GinnyAnswer
Let's break down the problem step by step to find the correct inequality to determine how many times Jimmy visited the student's home.

1. Identify the Fixed and Variable Charges:
- Jimmy charges a fixed amount of \[tex]$40 per semester for tutoring. - In addition to the fixed charge, he charges an extra \$[/tex]10 for each home visit. Let [tex]\( x \)[/tex] represent the number of home visits.

2. Establish the Total Earnings:
- The total amount Jimmy earns from tutoring one student would be the sum of the fixed semester charge and the additional charge for home visits.
- Hence, the total earnings can be represented by the expression: [tex]\( 40 + 10x \)[/tex].

3. Set Up the Inequality:
- Jimmy made less than \[tex]$80 this semester from tutoring one student. - So, the total earnings should be less than \$[/tex]80.

4. Formulate the Inequality:
- The inequality to represent this situation is: [tex]\( 40 + 10x < 80 \)[/tex].

Therefore, the correct inequality to determine how many times Jimmy visited the student's home is:

B. [tex]\( 40 + 10x < 80 \)[/tex]

Based on the detailed breakdown, this inequality correctly represents the scenario described in the problem.
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