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QuestionJody's brother is 3 years less than twice Jody's age. Their ages sum to 30. What is Jody's brother's age? Options: 19, 7, 23, 11.

Studdy Solution

STEP 1

Assumptions1. Let's denote Jody's age as J. . Jody's brother's age is three years less than twice Jody's age.
3. The sum of their ages is30.

STEP 2

First, we need to express Jody's brother's age in terms of Jody's age. According to the problem, Jody's brother's age is three years less than twice Jody's age. We can write this asBrother′s age=2J−Brother's\, age =2J -

STEP 3

Now, we know that the sum of their ages is30. We can express this as an equationJ+Brother′s age=30J + Brother's\, age =30

STEP 4

Substitute the expression for the brother's age from2 into the equation from3.
J+(2J−3)=30J + (2J -3) =30

STEP 5

implify the left side of the equation by combining like terms.
3J−3=303J -3 =30

STEP 6

Next, we use the addition property of equality to isolate the term with J on one side of the equation. We add3 to both sides of the equation.
3J−3+3=30+33J -3 +3 =30 +3

STEP 7

implify both sides of the equation.
3J=333J =33

STEP 8

Now, we use the multiplication property of equality to solve for J. We divide both sides of the equation by3.
J=33/3J =33 /3

STEP 9

implify the right side of the equation to find J.
J=11J =11

STEP 10

Now that we have Jody's age, we can find the age of Jody's brother by substituting J = into the equation from2.
Brother′s age=2()−3Brother's\, age =2() -3

STEP 11

Calculate the brother's age.
Brother′s age=22−3=19Brother's\, age =22 -3 =19So, the age of Jody's brother is19.

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