Question

Sadie is 3 years older than Kareem, and Kareem is twice as old as Nadra. The sum of their ages is 33.

A student used the steps below to find each person’s age.

Step 1 Write an equation, letting x represent Kareem’s age:
(x + 3) + x + 2 x = 33
Step 2 Solve the equation:
(x + 3) + x + 2 x = 33. 3 + 4 x = 33. 4 x = 30. x = 7 and one-half.
Step 3 Sadie is 10 and one-half, Kareem is 7 and one-half, and Nadra is 3 and three-fourths.

Which corrects the student’s first error?

Answer 1

Step 1-Write an equation, letting x represent Kareem’s age:

(x + 3) + x + 2 x = 33

Step 2-Solve the equation:

(x + 3) + x + 2 x = 33. 3 + 4 x = 33. 4 x = 30. x = 7 1/2.

Step 3-Sadie is 10 1/2, Kareem is 7 1/2, and Nadra is 3 3/4.

Which corrects the student’s first error?

1. In Step 1, the student should have used One-half x to represent Nadra’s age, and written the equation (x + 3) + x +1/2x = 33.

2. In Step 2, the student should have added 3 on both sides of the equation to find a solution of x = 9.

3. In Step 3, the solution represents Sadie’s age. Therefore, Sadie is 7 1/2, Kareem is 4 1/2, and Nadra is 2 1/4.

4. In Step 3, Nadra’s age is the difference between 33 and Sadie’s and Kareem’s ages, so Nadra is 15.