Question 521502
The ancient one is 40 years older than the youngster. 10 years agos, the age of the ancient one was 22 years greater than seven times the age of youngster then. How old are both of them today?


Let ancient's age be A, and youngster's, Y


Then, A = Y + 40 -------- eq (i)
A – 10 = 7(Y – 10) + 22 ----- A – 7Y = - 38 -------- eq (ii)


Y + 40 – 7Y = - 38 ------- Substituting Y + 40 for A in eq (ii) 
- 6Y = - 78
Y, or youngster = {{{(- 78)/- 6}}}, or {{{highlight_green(13)}}} years-old


A = 13 + 40 ------ Substituting 13 for Y in eq (i)
A, or ancient's age = {{{highlight_green(53)}}}


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Check
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Ancient is 40 years older than youngster
53 = 40 + 13
53 = 53 (TRUE)


10 years ago, ancient was 22 years older than 7 times youngster's age then


53 - 10 = 7(13 - 10) + 22


43 = 7(3) + 22


43 = 21 + 22


43 = 43 (TRUE)


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