In this problem, Sarah's income is quoted as an annual amount but her expenses are quoted as a monthly amount. In order to calculate her savings, she needs those units to both be in either "per year" or "per month." Since the variable  also represents a number of months, it is necessary for her to convert her annual salary into a monthly amount so that she can properly subtract expenses from income to reflect the amount of money saved. Therefore, dividing by 12 is how she makes that conversion.

To translate this appropriately, it can be helpful to slightly rephrase the topic from "medals won" to "total number of medals is."  If you say it as "Tina's total is more than twice George's total" the words directly line up to math symbols:

Tina's total: 

Is more than: 

George's total: 

So if Tina's total is more than twice George's total, that means that 

Note on this problem that the answer  is true - we know that Tina has more medals than George, so if we double her number of medals it's even a bigger mismatch. But it does not directly translate to the situation provided, so it's not the correct answer here as it does not perfectly answer the exact question.

This problem rewards your knowledge of both inequalities in general and the "or equal to" case specifically. The first mathematical statement you're given is that Tim must purchase "at least 20" items. "At least" means that it could be equal to, but also could be greater than, so you'd use the greater-than-or-equal-to sign, . This translates to .

The second mathematical statement you're given is that Tim must purchase more muffins than scones. Note that it is "more than" and not "at least as many as" so the correct sign to use is . You can set this up as , although this quickly translates to  as well.

The final statement is about cost. Since each scone costs $2.50 and each muffin costs $3, the costs can be summarized as . And you need this to be "no more than" $56.  "No more than" means that it could be equal to $56, or anything less, so you'll use the less-than-or-equal-to sign . This can be expressed as .

The amount of money that Clara spends will be a combination of the $1 she spends on each game and the $2.50 she spends on each ride. So her total expenditure can be expressed as , or more simply as .

Her constraint is that she is allowed to spend "up to $20" which means that she can spend any amount less than or equal to $20. So you'll use the less-than-or-equal-to sign, .

Therefore the correct answer is .

The two relationships you need to express are:

1) She sold fewer total boxes than her goal of 100, so her total  was less than . This is .

2) The total amount sold was greater than $1600. Her total amount sold is the price per box times the number of that box, or . If that was greater than $1600, your inequality is then .

There are two conditions to account for in this problem:

1) Bernard wants to work less than 20 hours. That means his total number of hours at both jobs  must be less than 20, which displays as .

2) Bernard wants his income to be at least $300. "At least" means "greater than or equal to" so you'll use the  sign. And his income will be his rate at each job times the number of hours he works at each. This makes this inequality 

This problem has two conditions. One is that Darius did achieve his total sales vehicles goal, and that one was to sell "at least" 50 vehicles. "At least" means greater than or equal to, so we'd use the inequality  here to indicate that he sold 50 or more vehicles to achieve that goal.

The second condition is a goal that he did not hit. The goal was to sell "more than $1,000,000." Here note that if he sold exactly $1,000,000 he would not have reached his goal of "more than $1,000,000" and of course if he sold less than $1,000,000 he would have missed his goal, too. So we can conclude that Darius sold less than or equal to $1,000,000. This means that you'd use the inequality .

Rashid's pay has two components: his earnings per hour, which we know is $20, and the number of hours he works, . To get his total pay, you multiply those together, so his total earnings are . We know that his total earnings were less than  $650, so we can use the inequality:

One important consideration for this problem is which inequality sign to use. Since Milt earns "at least as much" as Caitlyn, you should see that "at least" means "greater than or equal to," leading to this sign: 

You then have two total amounts: Milt's $12 per hour times his  hours per week, and Caitlyn's $15 per hour times her  hours per week.  Those are then , which is greater than equal to Caitlyn's total of . The correct answer is then .