Ratio Comparison and Angle Calculation Word Problems

Published on June 29, 2026

Pre-Algebra

Solve a ratio comparison problem for fruit baskets and calculate an unknown angle measure within a larger angle. Demonstrates understanding of ratios and angle properties.

Question

Answer

Based on the image provided, here are the step-by-step solutions for the two exercises.

Exercise 5

Problem:
A fruit basket contains 8 apples and 4 oranges. Another basket contains 12 apples and 6 oranges. Are the ratios of apples to oranges the same in both baskets? Show your work.

Step-by-step Solution:

Find the ratio for the first basket:
The ratio of apples to oranges is .
To simplify this ratio, divide both numbers by their greatest common divisor, which is 4:
Find the ratio for the second basket:
The ratio of apples to oranges is .
To simplify this ratio, divide both numbers by their greatest common divisor, which is 6:
Compare the ratios:
Since both simplified ratios are , the ratios are the same.

Final Answer:
Yes, the ratios of apples to oranges are the same in both baskets.

Exercise 6

Problem:

Draw an angle measuring .
Inside angle , draw the ray such that .
Are the angles and adjacent? Justify your answer.
Calculate the measure of angle .

Step-by-step Solution:

Drawing: (This is a construction step). You would draw a vertex , a ray , and a ray such that the opening between them is . Then, draw a ray starting from that splits the angle, placing such that the angle between and is .
Justification for adjacency:
Two angles are adjacent if they share a common vertex and a common side, and do not overlap.
- and share the common vertex .
- They share the common side (ray) .
- They do not overlap because ray is inside .
  Answer: Yes, they are adjacent.
Calculation of :
Since ray is inside , the sum of the two smaller angles equals the total angle:

Substitute the known values:

Subtract from both sides:

Final Answer:
The measure of angle

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