GED Math Practice Questions: Writing Inequalities
On the GED Mathematical Reasoning test, you may be asked to work with inequalities in word problems. In the following practice questions, you have to choose the inequality that most accurately expresses the situation in mathematical terms.
Cindy has $20 in her pocket and is heading to the fair. Admission is $3.50, and tickets for food and games are $1.00 each. Which of the following inequalities represents the number of tickets that Cindy can afford to buy if t represents the number of tickets?
David is a prolific stamp collector. When asked how large his collection is, he replies that he has nearly 2,000 stamps. He has 780 Canadian stamps and 910 U.S. stamps with an average value of $5.00 each, and 310 stamps from other countries around the world with an average value of less than $3.00 each. Which of the following inequalities most accurately expresses the total monetary value of David’s stamp collection if S represents the total value of his collection?
Answers and explanations
To answer questions such as this one, reason it out. Cindy starts with $20.00 and spends $3.50 getting in, so she now has $20.00–$3.50. She wants to buy t number of tickets at $1.00 each, making the total she ultimately spends on tickets $1.00t. The total she spends on tickets plus the admission price must be less than or equal to $20.00, which can be expressed as:
Unfortunately, that’s not one of the choices, but Choice (C) looks promising. The amount she can spend on tickets, $1.00t, must be less than or equal to the $20.00 she started with minus the $3.50 admission. Choice (C) is correct! By the way, Choice (D) is obviously incorrect because it’s not an inequality.
David has 780 + 910 = 1,690 total Canadian and U.S. stamps that average $5.00 each for a total of $8,450. Additionally, he has 310 stamps with an average value of less than $3.00, so the total value of those must be less than $930. $8,450 + $930 = $9,380, so the total value of his collection must be more than $8,450 and less than $9,380. Choice (E) is correct. Choice (F) has the possibility of the value being less than $8,450 and possibly exceeding $9,380. Choice (G) also has the possibility of the collection’s value exceeding $9,380. And Choice (H) has a range of values that’s too broad; although it’s correct, it’s not as accurate as Choice (E).