12. Strawbery Summer Fhonda and Nadine beth plek strawberries in the summer but for different companies. Rhonda earns \( \$ 3 \) for each basket she ploke Nadine earns \( \$ 1 \) per basket she picks plus \( \$ 20 \) for the day a) Write an equation to represent the income that each girl earns at their job, where \( E \) is their tatal earning for one day in dollars and \( n \) is the number of baskets of strawberries picked that day. Rhonda: \( \qquad \) Nadine: \[ E=1(n)+20 \] b) If they each pick 15 baskets of strawberries, who makes more money and by how much? Show your work \[ \begin{array}{l} \text { 'r thonda: } E=3(15), E=45 \$ \\ \text { Nadine: } E=1(15)+20, E=35 \$ \end{array} \] * rhonda earns more money c) If they each earn \$81, how many baskets of strawberries does eachgin pick? Show your work. Thond: \( 81=3(n), 81 \div 3=n,(n=27 \) Nadine: \( 81=1(n)+20,81-20=61 \) so \( n=61 \) e) Determine the point of intersection algebraically by substitution or elimination.
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Rhonda's earnings can be expressed with the equation \( E = 3n \), where \( n \) is the number of baskets picked. Nadine's equation, however, should include her flat day rate: \( E = n + 20 \). With these equations, we can easily see how their earnings compare based on the number of baskets picked! To find the point of intersection, we can set the two equations equal to each other: \[ 3n = n + 20 \] Subtracting \( n \) from both sides gives us \( 2n = 20 \), so dividing both sides by 2 gives \( n = 10 \). Substituting back in, \( E = 3(10) = 30 \) for Rhonda, and \( E = 10 + 20 = 30 \) for Nadine. Thus, they intersect at \( (10, 30) \).