Age problem

Algebra Level 2

Five years hence the age of Tris's father Andrew Prior will be three times that of her. Five years ago Andrew's age was seven times that of Tris. What is Tris's age?

15 13 10 16

Vishwathiga Jayasankar by vishwathiga jayasankar , 20, India

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1 solution

Pham Khanh
Apr 21, 2016

Call A A is the age of Andrew, T T is the age of Tris. So we have this system of equations: A + 5 = 3 × T + 15 A − 5 = 7 × T − 35 \begin{aligned} \color{#D61F06}{A}+5 & = & 3 \times \color{#20A900}{T}+15 \\ \color{#D61F06}{A}-5 & = & 7 \times \color{#20A900}{T}-35 \end{aligned} ⟹ ( A + 5 ) − ( A − 5 ) = ( 3 × T + 15 ) − ( 7 × T − 35 ) \implies (\color{#D61F06}{A}+5)-(\color{#D61F06}{A}-5)=(3 \times \color{#20A900}{T}+15)-(7 \times \color{#20A900}{T}-35) ⟺ 10 = − 4 × T + 50 \iff 10=-4 \times \color{#20A900}{T}+50 ⟺ − 4 × T = 10 − 50 = − 40 \iff -4 \times \color{#20A900}{T}=10-50=-40 ⟺ T = − 40 − 4 = 10 \iff \color{#20A900}{T}=\frac{-40}{-4}=10 Hence, the answer is T r i s i s 10 y e a r s o l d \LARGE \color{#624F41}{\boxed{\color{#20A900}{Tris~is~10~years~old}}}

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