Respuesta :
We define the following variables:
• m = m(x,y) = money earned,
,• x = number of hours worked,
,• y = number of programs made.
From the statement, we know that Sandra earns:
• $17.25 per hour by writing computer programs,
• $75 for every program that she finishes.
Using this data, we write the following equation for the money earned:
[tex]m(x,y)=\text{ \$17.25 }\cdot x+\text{ \$75 }\cdot y.[/tex]We know that she earned m = $813, and she worked x = 8 hours. We want to know how many programs she made (y). To do that, we replace these data in the equation above, so we have:
[tex]\text{ \$}813=\text{ \$17.25}\cdot8+\text{ \$75}\cdot y.[/tex]Solving for the variable y, we get:
[tex]\begin{gathered} 813=17.25\cdot8+75\cdot y, \\ 813=138+75\cdot y, \\ 75\cdot y=813-138, \\ 75\cdot y=675, \\ y=\frac{675}{75}=9. \end{gathered}[/tex]We have that Sandra made y = 9 programs in her shift.
Answer
Sandra made 9 programs in her shift.
