IAAT - Iowa Algebra Aptitude Solving Word Problems Questions and Answers

Question 1

The sum of three consecutive odd integers is 87. What is the largest of the three integers?

Accepted Answer

31

Answer

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?

Accepted Answer

s + 2s = 24

Answer

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?

Accepted Answer

4 hours

Answer

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?

Accepted Answer

0.75p - 10

Answer

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?

Accepted Answer

216 sq ft

Answer

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.

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Solving Word Problems Questions and Answers