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# Arthur and his son's age

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Four years ago Arthur is 11 times as old as his son Arthur Jr, but four years from now, Arthur will only be 3 times as old as Jr. What is Arthur’s age when he is twice as old as Arthur Jr?

Jan 11, 2021

#1
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Arthur's age is 50 when he is twice as old as Arthur Jr.

Jan 11, 2021
#2
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Four years ago Arthur is 11 times as old as his son Arthur Jr,
but four years from now, Arthur will only be 3 times as old as Jr.
What is Arthur’s age when he is twice as old as Arthur Jr?

$$\text{Let Arthur =a} \\ \text{Let his son Arthur Jr =j}$$

$$\begin{array}{|lrcll|} \hline 1. & \mathbf{a-4} &=& \mathbf{11(j-4)} \\ & a &=& 11(j-4) + 4 \\ & a &=& 11j-44 + 4 \\ & \mathbf{a} &=& \mathbf{11j-40} \\ \hline \end{array}$$

$$\begin{array}{|lrcll|} \hline 2. & \mathbf{a+4} &=& \mathbf{3(j+4)} \\ & a &=& 3(j+4) - 4 \\ & a &=& 3j+12 - 4 \\ & a &=& 3j+8 \quad | \quad \mathbf{a=11j-40} \\ & 11j-40 &=& 3j+8 \\ & 11j-3j &=& 3j+8+40 \\ & 8j &=& 48 \quad | \quad : 8 \\ & \mathbf{j} &=& \mathbf{6} \\ \hline & \mathbf{a} &=& \mathbf{11j-40} \quad | \quad j=6 \\ & a &=& 11*6 - 40 \\ & a &=& 66-40 \\ & \mathbf{a} &=& \mathbf{26} \\ \hline \end{array}$$

$$\begin{array}{|lrcll|} \hline 3. & \mathbf{a+x} &=& \mathbf{2(j+x)} \\ & a &=& 2(j+x) - x \\ & a &=& 2j + 2x - x \\ & a &=& 2j + x \\ & x &=& a-2j \quad | \quad a=26~j=6 \\ & x &=& 26-2*6 \\ & x &=& 26-12 \\ & x &=& 14 \\ \hline \end{array}$$

14 years from now, Arthur will be $$26+14=\mathbf{40}$$ years old.
14 years from now, his son Arthur Jr will be $$6+14=\mathbf{20}$$ years old.
Arthur’s age is then twice as old as Arthur Jr

Jan 11, 2021
#3
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a = arthur     j = junior

a-4 = 11 (j-4)

a = 11j -40

a+4 = 3 (j+4)

a = 3j +8                      equate the two red equations and solve for j = 6    then a= 3j+8  = 26

26+x = 2 (6+x)    solve for x = 14       Arthur will be 26+14 = 40 y/o   when son is 20 y/0

Jan 11, 2021