Miguel and Grace started collecting rare coins at the same time. Back then, they had the same number of rare coins. Miguel has been collecting 5 coins each week and he now has 38 coins. Grace has been collecting 3 coins each week and she now has 24 coins. How many rare coins did they have all together when they started collecting?

Question

A. 33
B. 66
C. 77
D. 14

Answer 1

Miguel has been collecting coins for 38 / 5 = <<38/5=7.6>>7.6 weeks
Grace has been collecting coins for 24 / 3 = <<24/3=8>>8 weeks.
So, the less time Miguel spent collecting coins equals to Grace's time collecting coins for 8 - 7.6 = <<8-7.6=0.4>>0.4 weeks.
Since time eventually catches up, we can consider that Miguel and Grace are collecting coins for the same time.
Knowing that Miguel and Grace have been collecting coins for 7.6 weeks, together, they have collected a number of coins equal to 7.6 * (5 + 3) = 7.6 * 8 = <<7.6*8=60.8>>60.8
Now, rounded to the nearest whole number, their total number of coins comes down to 61.
That means that when they started collecting coins, Miguel and Grace had a number of coins equal to 61. Answer: \boxed{61}.