IAAT - Iowa Algebra Aptitude Solving Word Problems Questions and Answers — Questions and Answers
Question 1: The sum of three consecutive odd integers is 87. What is the largest of the three integers?
- 27
- 29
- 31 (Correct answer)
- 33
Correct answer: 31
Let the smallest odd integer be represented by 'n'. Since consecutive odd integers are 2 apart, the next two are 'n + 2' and 'n + 4'. The sum is n + (n + 2) + (n + 4) = 87. Combining like terms gives 3n + 6 = 87. Subtracting 6 from both sides gives 3n = 81. Dividing by 3 gives n = 27. The three integers are 27, 29, and 31. The largest of these is 31.
Question 2: Maria is twice as old as her brother, Sam. The sum of their ages is 24. Which equation can be used to find Sam's age, s?
- s + 2 = 24
- 2s = 24
- s(2s) = 24
- s + 2s = 24 (Correct answer)
Correct answer: s + 2s = 24
Let 's' be Sam's age. The problem states Maria is twice as old as Sam, so Maria's age can be represented as '2s'. The sum of their ages is 24, which translates to the equation: Sam's age + Maria's age = 24, or s + 2s = 24.
Question 3: Two cyclists start from the same point and travel in opposite directions. One cyclist travels at a speed of 12 miles per hour (mph), and the other travels at 15 mph. After how many hours will they be 108 miles apart?
- 3 hours
- 4 hours (Correct answer)
- 4.5 hours
- 9 hours
Correct answer: 4 hours
When two objects move in opposite directions, their speeds add up to determine the rate at which the distance between them increases. Their combined speed is 12 mph + 15 mph = 27 mph. To find the time it takes for them to be 108 miles apart, use the formula Distance = Rate × Time. So, 108 = 27 × Time. Dividing both sides by 27 gives Time = 108 / 27 = 4 hours.
Question 4: A jacket's original price is represented by 'p'. It is on sale for 25% off. A customer has an additional coupon for $10 off the sale price. Which expression represents the final price the customer pays?
- 0.25p - 10
- p - 0.25 - 10
- 0.75p - 10 (Correct answer)
- p - 10.25
Correct answer: 0.75p - 10
First, calculate the sale price. A 25% discount means the customer pays 75% of the original price (100% - 25% = 75%). This is represented as 0.75p. After the discount is applied, the $10 coupon is used. This means you subtract $10 from the sale price. The final expression is 0.75p - 10.
Question 5: The length of a rectangular garden is 6 feet longer than its width. If the perimeter of the garden is 60 feet, what is the area of the garden in square feet?
- 144 sq ft
- 225 sq ft
- 216 sq ft (Correct answer)
- 252 sq ft
Correct answer: 216 sq ft
Let 'w' be the width. The length 'l' is w + 6. The formula for the perimeter of a rectangle is P = 2l + 2w. Substitute the given values: 60 = 2(w + 6) + 2w. Distribute the 2: 60 = 2w + 12 + 2w. Combine like terms: 60 = 4w + 12. Subtract 12 from both sides: 48 = 4w. Divide by 4: w = 12 feet. The length is l = 12 + 6 = 18 feet. The area is A = l × w = 18 × 12 = 216 square feet.
Question 6: A person has 20 coins consisting of only dimes and quarters. The total value of the coins is $3.20. Which system of equations can be used to find the number of dimes (d) and quarters (q)?
- d + q = 3.20 AND 0.10d + 0.25q = 20
- d + q = 20 AND 10d + 25q = 3.20
- d + q = 20 AND 0.10d + 0.25q = 3.20 (Correct answer)
- d + q = 5.20 AND d + q = 20
Correct answer: d + q = 20 AND 0.10d + 0.25q = 3.20
The problem can be described by two separate relationships, leading to two equations. The first is about the quantity of coins: the number of dimes (d) plus the number of quarters (q) equals 20. This gives the equation d + q = 20. The second is about the total value: the value of the dimes (0.10d) plus the value of the quarters (0.25q) equals $3.20. This gives the equation 0.10d + 0.25q = 3.20.
IAAT - Iowa Algebra Aptitude Solving Word Problems Questions and Answers
The sum of three consecutive odd integers is 87.
What is the largest of the three integers?