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Sue works weekdays for $10 an hour, Saturdays for $15 an hour, and Sundays for $20 an hour. If she worked 180 hours last month and earned $2315, how many more weekday hours than Sunday hours did she work last month?​

Sagot :

Answer: $1967

Step-by-step explanation:

semsee45

Answer:

77 hours

Step-by-step explanation:

Sue works:

  • Weekdays for $10 an hour.
  • Saturdays for $15 an hour.
  • Sundays for $20 an hour.

The question suggests that Sue only worked weekdays and Sundays last month as it does not mention Saturday hours.

Assign variables:

  • Let x = number of weekday hours Sue worked last month.
  • Let y = number of Sunday hours Sue worked last month.

Create two equations with the given information and defined variables:

[tex]\textsf{Equation 1}: \quad x + y = 180[/tex]

[tex]\textsf{Equation 2}: \quad 10x+20y=2315[/tex]

Rewrite the first equation to isolate x:

[tex]\implies x+y-y=180-y[/tex]

[tex]\implies x=180-y[/tex]

Substitute the found expression for x into the second equation and solve for y:

[tex]\implies 10(180-y)+20y=2315[/tex]

[tex]\implies 1800-10y+20y=2315[/tex]

[tex]\implies 1800+10y=2315[/tex]

[tex]\implies 1800+10y-1800=2315-1800[/tex]

[tex]\implies 10y=515[/tex]

[tex]\implies 10y \div 10=515 \div 10[/tex]

[tex]\implies y=51.5[/tex]

Substitute the found value of y into the first equation and solve for x:

[tex]\implies x+51.5=180[/tex]

[tex]\implies x+51.5-5.15=180-51.5[/tex]

[tex]\implies x=128.5[/tex]

Therefore, Sue worked:

  • 128.5 weekday hours
  • 51.5 Sunday hours

To find how many more weekday hours than Sunday hours Sue worked last month, simply subtract the found number of Sunday hours from the found number of weekday hours:

[tex]\implies 128.5-51.5 =77[/tex]

Therefore, Sue worked 77 more weekday hours than Sunday hours last month.

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