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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?
In Step 1, the student should have used One-half x to represent Nadra’s age, and written the equation (x + 3) + x + one-half x = 33.
In Step 2, the student should have added 3 on both sides of the equation to find a solution of x = 9.
In Step 3, the solution represents Sadie’s age. Therefore, Sadie is 7 and one-half, Kareem is 4 and one-half, and Nadra is 2 and one-fourth.
In Step 3, Nadra’s age is the difference between 33 and Sadie’s and Kareem’s ages, so Nadra is 15.
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