Question

Bill will run at least 31 miles this week. So far, he has run 16 miles. What are the possible numbers of additional miles he will run? Use t for the number of additional miles he will run. Write your answer as an inequality solved for t.

Answer 1

The inequality to set up is
`t+16 \ge 31`

It solves to
`t \ge 15`

Bill needs to run at least 15 more miles.

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Step-by-step explanation:

He has run 16 miles so far. Add on another t miles to get 16+t or t+16 to represent the total amount he runs. This expression must be 31 or larger

Either t+16 > 31 or t+16 = 31

Those two items condense to
`t+16 \ge 31`

To solve for t, we subtract 16 from both sides to undo the +16.

`t+16 \ge 31\\\\t+16-16 \ge 31-16\\\\t \ge 15\\\\`

Bill needs to run at least 15 more miles.

Meaning that t = 15, t = 16, t = 17, etc.