Julie bought 72 donuts in total. Both solution methods, using a diagram and algebraic equations and both methods, though different in approach, are interconnected.
How to find amount?
Count the total number of shaded slices (jelly + cinnamon + glazed) to determine the total number of donuts.
Total donuts = Jelly donuts + Cinnamon donuts + Glazed donuts
Total donuts = 1/6 + 1/3 + 5/6
= 2+2+5
= 9 donuts
Solution with Algebraic Equations
Let x represent the total number of donuts.
Jelly donuts: 1/6x = ?
Cinnamon donuts: 1/3x = ?
Glazed donuts: 5/6(x - 1/6x - 1/3x) = 20
Solve for x. From the glazed donuts equation:
5/6(x - 1/6x - 1/3x) = 20
5/6(2/3x) = 20
5x/18 = 20
x = 20 × 18/5
x = 72
Therefore, Julie bought 72 donuts in total.
Relationship between the Two Solution Methods
Both solution methods, using a diagram and algebraic equations, effectively solve the same problem but approach it from different perspectives. The diagram method provides a visual representation of the problem. On the other hand, the algebraic method relies on mathematical equations.
Both methods, though different in approach, are interconnected. The diagram can be used to visualize the algebraic equations, and the algebraic equations can be used to quantify the information depicted in the diagram.