Question

warm-up
here is a shape puzzle. the sum of each row and column is shown.
determine the value of each heart and sun.
(image shows a 3x3 grid of shapes: first row has sun, star (3), sun with sum 31; second row has heart (6), star (3), star (3) with sum 12; third row has sun, heart (6), sun with sum 34. also a table with shape (heart, star, sun) and value (heart: 6, star: 3, sun: blank) and a try it button.)

Explanation:

Step1: Analyze the third row

The third row is Sun + Heart + Sun = 34. We know Heart = 6, so substitute: \( 2 \times \text{Sun} + 6 = 34 \)

Step2: Solve for Sun

Subtract 6 from both sides: \( 2 \times \text{Sun} = 34 - 6 = 28 \)
Divide by 2: \( \text{Sun} = \frac{28}{2} = 14 \)

Answer:

14