Final answer:
The algebraic equation that represents the model ⋅27=33⋅10 is 2n+7=3n+3. Simplifying this we find the solution n=4.
Step-by-step explanation:
The question provided is asking which algebraic equation represents the algebra tiles model that corresponds to the given multiplication ⋅27=33⋅10. To determine the correct equation, we compare the algebraic expressions that could represent the algebra tiles model: option a) 2n−7=3n−3 and option b) 2n+7=3n+3.
If we interpret the multiplication ⋅ as indicating an equation, the ⋅27 on the left side can be viewed as representing '2n minus 7,' and 33⋅10 as '3n plus 3.' Thus, the correct equation that represents this model is b) 2n+7=3n+3.
To eliminate terms wherever possible and simplify the equation, we can subtract 2n from both sides to get 7=n+3. Then subtracting 3 from both sides, we end up with n=4 as the solution to the equation.
In the equation ⋅27=33⋅10, the left-hand side represents the area of a rectangle with length 27 and unknown width. The right-hand side represents the area of a rectangle with length 33 and width 10.
By setting the two areas equal to each other, we get 27 = 33w, which simplifies to 2n+7=3n+3.
The equation that represents the given algebra tiles model is option b) 2n+7=3n+3