Divide money amounts: word problems

Learning Objectives Identify the scale factor between two similar figures from given linear dimensions. Determine whether a word problem requires a ratio of lengths, areas, or volumes. Apply the correct ratio (k, k², or k³) to set up a proportion for dividing a sum of money. Solve multi-step word problems involving the division of money based on the principles of geometric similarity. Translate a real-world scenario about fair division into a mathematical model using similarity. Justify their method for dividing money by referencing the relationship between the scale factor and the ratios of area and volume. Two friends are paid $500 to paint two mathematically similar murals, one of which is twice as tall as the other. Should they split the money evenly? 🤔 This lesson con...

TermDefinitionExample Similar PolygonsPolygons that have the same shape but may be different in size. Their corresponding angles are congruent, and the ratios of their corresponding side lengths are equal.A 3-4-5 right triangle is similar to a 6-8-10 right triangle because all corresponding angles are equal and the ratio of corresponding sides is 1:2. Scale Factor (k)The constant ratio of any two corresponding linear measurements (like side length, height, or perimeter) of two similar figures.If Triangle A has a side of length 5 and the corresponding side of similar Triangle B is 15, the scale factor from A to B is k = 15/5 = 3. Ratio of PerimetersIf two similar figures have a scale factor of k, then the ratio of their perimeters is also k.A 3x5 rectangle (Perimeter=16) and a similar 6x10...

Ratio of Areas of Similar Figures If the scale factor of two similar figures is \( \frac{a}{b} \), then the ratio of their areas is \( (\frac{a}{b})^2 = \frac{a^2}{b^2} \). Use this rule when dividing money based on a two-dimensional quantity, such as the amount of paint needed, the area of land farmed, or the fabric used for a flag. Ratio of Volumes of Similar Figures If the scale factor of two similar solids is \( \frac{a}{b} \), then the ratio of their volumes is \( (\frac{a}{b})^3 = \frac{a^3}{b^3} \). Use this rule when dividing money based on a three-dimensional quantity, such as the amount of material in a sculpture, the capacity of a container, or the weight of a solid object. Proportional Division Formula To divide a total amount \( T \) in a ratio \( a:b \),...