Cedric plans to ride his bicycle 2 miles to a park and then ride several times around a loop in the park that is 5 miles long. then he'll ride the same way home. he wants to ride a total of at least 19 miles. the inequality 5t+4> 19 models this situation, where t is the number of times cedric rides around the loop. solve the inequality. how many times does cedric need to ride around the loop? a. 3 or more times b. at most 4 c. at most 3 times d. 4 or more times

Hello!

Don't let the mumbojumbo of the word problem throw you off. We have here the inequality 5t+4>19

so solving for unknown variable t which is number laps we get,

5t+4-4>19-4 subtracting 4 from both sides we are left with 

5t>15 so now we divided both sides by 5 to get t alone and we have 

t>15/5= t>3 laps so C is the answer. He must ride 3 laps to ride at least 19 miles

Hope this helps! Any questions please feel free to ask! Thank you much!

I am doing the procedure to get the inequality because it is important to realize that the symbol to use is ≥, given that the problem states that the number of miles is at least 19, so 19 is a valid number of miles.

option 3 or more times

Explanation:

1) First, I would like to explain how to get the inequality:

Cedric plans to ride his bicycle 2 miles to a park and then ride several times around a loop in the park that is 5 miles long.

number of times around the loop of 5 miles long: t

number of miles around the loop: 5t

number of miles from home to the park and from park to home: 2 + 2 = 4.

total number of miles: 5t + 4

He wants to ride a total of at least 19 miles => 5t+4 ≥ 19

So the inequality that models this situation is 5t + 4 ≥ 19 (notice that the inequality simbol is ≥ and not >)

2) Now we can solve the inequality, with a better understanding of what it means.

5t ≥ 19 - 4

5t ≥ 15

t ≥ 15 / 5

t ≥ 3

Then, the right answer is the option 3 or more times