Let's denote the number of hours you worked on Sunday as \( x \) and the number of hours your sister worked on Sunday as \( y \).
You earn four dollars per hour, and your sister earns five dollars per hour, and together you worked a total of seven hours. So we have the following equations:
- \( x + y = 7 \) (total hours worked)
- \( 4x + 5y = 32 \) (total earnings)
Now we can solve these equations. From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 7 - x \]
Next, we can substitute this expression for \( y \) into the second equation:
\[ 4x + 5(7 - x) = 32 \]
Distributing the 5:
\[ 4x + 35 - 5x = 32 \]
Combining like terms:
\[ -1x + 35 = 32 \]
Subtracting 35 from both sides:
\[ -1x = 32 - 35 \] \[ -1x = -3 \]
Dividing by -1:
\[ x = 3 \]
Now substituting \( x \) back into the equation for \( y \):
\[ y = 7 - x = 7 - 3 = 4 \]
So you worked 3 hours and your sister worked 4 hours on Sunday.
Now, we can calculate your earnings:
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Your earnings: \[ 4 , \text{dollars/hour} \times 3 , \text{hours} = 12 , \text{dollars} \]
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Your sister's earnings: \[ 5 , \text{dollars/hour} \times 4 , \text{hours} = 20 , \text{dollars} \]
Thus, you earned $12 on Sunday, and your sister earned $20 on Sunday.
If you want to know how much you each earned on Saturday as well, we need to know the total hours worked on Saturday, which is not provided. If you worked the same total hours across the weekend, then we would need that information to calculate Saturday's earnings.
If you did not work on Saturday and only on Sunday, you each earned only from Sunday. Please clarify if more information is needed!
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