Mark, Jessica & Nate each downloaded music from the same website. Mark downloaded 10 songs in total consisting of pop, rock,
& hip hop. Jessica downloaded 5 times as many pop songs, twice as many rock and 3 times as many hip hop songs as Mark. She downloaded 28 songs total. If Nate downloaded 20 songs total with 3 times as many pop songs, 3 times as many rock songs, and the same number of hip hop songs as Mark, how many songs of each type did Mark download?
P + r + h = 10 <== mark 5p + 2r + 3h = 28 <== jessica 3p + 3r + h = 20 <== nate
p + r + h = 10 3p + 3r + h = 20...multiply by -1 -------------------- p + r + h = 10 -3p - 3r - h = -20 (result of multiplying by -1) -------------------add -2p - 2r = -10
p + r + h = 10...multiply by -3 5p + 2r + 3h = 28 --------------------- -3p - 3r - 3h = -30 (result of multiplying by -3) 5p + 2r + 3h = 28 --------------------add 2p - r = -2
-2p - 2r = -10 2p - r = -2 ---------------add -3r = -12 r = -12/-3 r = 4
2p - r = -2 2p - 4 = -2 2p = -2 + 4 2p = 2 p = 1
p + r + h = 10 1 + 4 + h = 10 5 + h = 10 h = 10 - 5 h = 5
Jessica downloaded : 5p + 2r + 3h = 28 5(1) + 2(4) + 3(5) = 28 5 + 8 + 15 = 28 28 = 28 (correct)......she got 5 pop, 8 rock, and 15 hip hop
Nate downloaded : 3p + 3r + h = 20 3(1) + 3(4) + 5 = 20 3 + 12 + 5 = 20 20 = 20 (correct)...he got 3 pop, 12 rock, and 5 hip hop
Mark downloaded : p + r + h = 10 1 + 4 + 5 = 10 10 = 10 (correct)....he got 1 pop, 4 rock, and 5 hip hop <===
60.5 milligrams per square centimeter First, determine how many half lives have expired by dividing the time by the half-life. So: 55/20 = 2.75 That means that only 2^(-2.75) = 0.148650889 = 14.8650889% of the original substance remains. So just divide the amount remaining by 0.148650889 to get the original amount. 9 / 0.148650889 = 60.5445419 So originally, there was 60.5 milligrams per square centimeter 55 years ago.
