Tommy is going to be participating in a long bike race soon. He needs to ride a total of at least $119$ kilometers today. He plans to do this by riding multiple laps on the Highland Loop, which is $17$ kilometers long, and the Pinehurst Loop, which is $49$ kilometers long. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of laps on the Highland Loop $\newline$ $y =$ the number of laps on the Pinehurst Loop $\newline$ Choices: $\newline$ (A) $17x + 49y > 119$ $\newline$ (B) $49x + 17y \geq 119$ $\newline$ (C) $49x + 17y > 119$ $\newline$ (D) $17x + 49y \geq 119$

Full solution

Q. Tommy is going to be participating in a long bike race soon. He needs to ride a total of at least

119

kilometers today. He plans to do this by riding multiple laps on the Highland Loop, which is

17

kilometers long, and the Pinehurst Loop, which is

49

kilometers long.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of laps on the Highland Loop

\newline

y =

the number of laps on the Pinehurst Loop

\newline

Choices:

\newline

(A)

17x + 49y > 119

\newline

(B)

49x + 17y \geq 119

\newline

(C)

49x + 17y > 119

\newline

(D)

17x + 49y \geq 119

Identify Required Distance: Tommy needs to ride at least $119$ kilometers, so we're looking for an inequality that represents this. The Highland Loop is $17$ kilometers long, and the Pinehurst Loop is $49$ kilometers long. If $x$ is the number of laps on the Highland Loop and $y$ is the number of laps on the Pinehurst Loop, then the total distance Tommy rides is $17x + 49y$ . Since he needs to ride at least $119$ kilometers, the inequality should reflect that the total distance is greater than or equal to $119$ .
Formulate Inequality: We write the inequality as $17x + 49y \geq 119$ , because Tommy can ride exactly $119$ kilometers or more. This inequality shows that the total distance covered by riding $x$ laps of the Highland Loop and $y$ laps of the Pinehurst Loop should be at least $119$ kilometers.
Check Given Choices: Now we check the choices given to see which one matches our inequality. Choice (A) says $17x + 49y > 119$ , but this means Tommy would have to ride more than $119$ kilometers, which is not what's required; he just needs to ride at least $119$ kilometers. Choice (B) says $49x + 17y \geq 119$ , but this has the coefficients for $x$ and $y$ swapped. Choice (C) says $49x + 17y > 119$ , which also has the coefficients swapped and indicates more than $119$ kilometers. Choice (D) says $17x + 49y \geq 119$ , which matches our inequality exactly.