Each side of a 30-sided polygon has one ofthree lengths. The number of sides with length8 centimeters (cm) is 5 times the number of sides nwith length 3 cm. There are 6 sides with length 4 cm.Which equation must be true for the value of n ?A) 5n+6=30B) 6n+6= 30C) 8n+ 3n + 4n = 30D) 8(5n) + 3n + 4(6) = 30
Question
Each side of a 30-sided polygon has one ofthree lengths. The number of sides with length8 centimeters (cm) is 5 times the number of sides nwith length 3 cm. There are 6 sides with length 4 cm.Which equation must be true for the value of n ?A) 5n+6=30B) 6n+6= 30C) 8n+ 3n + 4n = 30D) 8(5n) + 3n + 4(6) = 30
Solution
The correct equation that must be true for the value of n is A) 5n+6=30.
Here's why:
The problem states that the polygon has 30 sides. It also states that the number of sides with length 8 cm is 5 times the number of sides with length 3 cm (which we'll call n).
So, the number of sides with length 8 cm is 5n.
The problem also states that there are 6 sides with length 4 cm.
So, the total number of sides is the number of sides with length 8 cm (5n) plus the number of sides with length 3 cm (n) plus the number of sides with length 4 cm (6).
This gives us the equation 5n + n + 6 = 30.
Simplifying this equation gives us 5n + 6 = 30, which matches option A.
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