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20) Two numbers a and b are in the ratio of 3:4. If the first number is increased by 2 and the second number is decreased by 4, they are in the ratio of 7:8. Find a and b.

20) Two numbers a and b are in the ratio of 3:4. If the first number is increased by 2 and the second number is decreased by 4, they are in the ratio of 7:8. Find a and b.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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do 20 please

**Geometry and Algebra Problems** --- ### 19) Geometry Problem: Kite Area Calculation Given: - Kite \(ABCD\) with \(BD = 10\) - \( \angle BAC = 45^\circ\) - \( \angle BCA = 30^\circ\) Find: Area of the kite \(ABCD\) *Explanation with Diagram:* In the provided diagram, Kite \(ABCD\) is illustrated with diagonals \(AC\) (horizontal) and \(BD\) (vertical). The diagonals intersect at right angles (90 degrees) forming right triangles. Diagram: ``` B / \ / \ A-----C \ / \ / D ``` Parameters: - Diagonal \(BD\) (vertical) = 10 units - \( \angle BAC = 45^\circ\) - \( \angle BCA = 30^\circ\) --- ### 20) Algebra Problem: Finding Numbers in a Ratio Two numbers \(a\) and \(b\) are in the ratio of 3:4. If the first number is increased by 2 and the second number is decreased by 4, they are in the ratio of 7:8. Find \(a\) and \(b\). *Step-by-Step Solution:* 1. Initial Ratio: \( \frac{a}{b} = \frac{3}{4}\) 2. Adjusted numbers: \( \frac{a+2}{b-4} = \frac{7}{8} \) Using these equations, solve for the values of \(a\) and \(b\). --- For educational materials, diagrams and their explanations aid in understanding geometric properties and the solving of algebraic ratios enhances problem-solving skills.
Transcribed Image Text:**Geometry and Algebra Problems** --- ### 19) Geometry Problem: Kite Area Calculation Given: - Kite \(ABCD\) with \(BD = 10\) - \( \angle BAC = 45^\circ\) - \( \angle BCA = 30^\circ\) Find: Area of the kite \(ABCD\) *Explanation with Diagram:* In the provided diagram, Kite \(ABCD\) is illustrated with diagonals \(AC\) (horizontal) and \(BD\) (vertical). The diagonals intersect at right angles (90 degrees) forming right triangles. Diagram: ``` B / \ / \ A-----C \ / \ / D ``` Parameters: - Diagonal \(BD\) (vertical) = 10 units - \( \angle BAC = 45^\circ\) - \( \angle BCA = 30^\circ\) --- ### 20) Algebra Problem: Finding Numbers in a Ratio Two numbers \(a\) and \(b\) are in the ratio of 3:4. If the first number is increased by 2 and the second number is decreased by 4, they are in the ratio of 7:8. Find \(a\) and \(b\). *Step-by-Step Solution:* 1. Initial Ratio: \( \frac{a}{b} = \frac{3}{4}\) 2. Adjusted numbers: \( \frac{a+2}{b-4} = \frac{7}{8} \) Using these equations, solve for the values of \(a\) and \(b\). --- For educational materials, diagrams and their explanations aid in understanding geometric properties and the solving of algebraic ratios enhances problem-solving skills.
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