A student loss 2/5 of his money during the break time,but then found 3/5of the amount lost.if he now had #252,how much was his original money

Question

Nigeria,k wara state

Answer 1

Let's break this problem down as simply as possible. The student's original amount of money is M. If he loses 2/5 of his money, he lost (2/5)*M. If he finds 3/5 of the original amount, he found 3/5 of 2/5 of M, or (3/5)*(2/5)*M. Let's restate his financial history using algebra:

• original amount MINUS amount lost PLUS amount found EQUALS 252
• M - (2/5)*M + (3/5)*(2/5)*M = 252 : (restated as algebra equation)
• M - (2/5)*M + (6/25)*M = 252 : (solve for (3/5)*(2/5))
• (25/25)*M - (10/25)*M + (6/25)*M = 252 : (restate all terms as 25ths so that they're easier to add)
• ((25 - 10 + 6)/25)*M = 252 : (add the 25ths terms together)
• (21/25)*M = 252 : (addition)
• (21/25)*M*(25/21) = 252*(25/21) : (multiply both sides by 25/21)
• M = 252*(25/21) : (simplify the left side)
• M = 300 : (simplify the right side)

 

Thus, we deduce that the student originally had 300. We can verify this answer using the following logic:

• Student originally had 300
• Student lost 2/5 of his original 300, or 120
• Student found 3/5 of the 120 he lost, or 72
• 300 - 120 + 72 = 252