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QuestionLet your brother's age be xx. Then your cousin's age is x+8x + 8. Three years ago, x+8−3=2(x−3)x + 8 - 3 = 2(x - 3). Find xx.

Studdy Solution

STEP 1

Assumptions1. Your cousin is8 years older than your brother. . Three years ago, your cousin was twice as old as your brother.
Let's denote the current age of your cousin as C and the current age of your brother as B.

STEP 2

We can express the first assumption as an equationC=B+8C = B +8

STEP 3

We can express the second assumption as an equation as well. Three years ago, your cousin was C -3 years old and your brother was B -3 years old. At that time, your cousin was twice as old as your brother, soC−3=2(B−3)C -3 =2(B -3)

STEP 4

Now we have a system of two equations\begin{align*} C &= B +8 \\ C -3 &=2(B -3) \end{align*}

STEP 5

We can simplify the second equationC−3=2B−C -3 =2B -

STEP 6

Rearranging the equation, we getC=2B−3C =2B -3

STEP 7

Now we have another system of two equations\begin{align*} C &= B + \\ C &=2B -3\end{align*}

STEP 8

Since both equations are equal to C, we can set them equal to each otherB+8=2B−3B +8 =2B -3

STEP 9

Rearranging the equation, we get8+3=2B−B8 +3 =2B - B

STEP 10

olving the equation, we findB=B =

STEP 11

Substitute B =11 into the first equationC=11+8C =11 +8

STEP 12

olving the equation, we findC=19C =19Your cousin is19 years old and your brother is11 years old.

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