[tex]E = \frac{4M}{3} \\E + 48 = 2(M+13)\\E + 48 = 2M + 26\\\frac{4M}{3}+48 = 2M + 26\\4M + 144 = 6M + 78\\2M = 66\\M = 33[/tex]
At the beginning, Malik had 33 beads, and Eric had 44, making them have 77 beads in total
At the end, Malik had (33 + 13 =) 46 beads and Eric had (44 + 48 = ) 92 beads.
Answer: they collected 77 beads all together.
Step-by-step explanation:
Let x represent the number of beads that Eric collected.
Let y represent the number of beads that Malik collected.
Eric collected 1 1/3(4/3) times as many beads as Malik in the beginning. This means that
x = 4y/3
If Eric collected 48 more beads and Malik collected 13 more beads, Eric would have twice as many beads as Malik. This means that
x + 48 = 2(y + 13)
x + 48 = 2y + 26 - - - - - - - - - - -1
Substituting x = 4y/3 into equation 1, it becomes
4y/3 + 48 = 2y + 26
Cross multiplying by 3, it becomes
4y + 144 = 6y + 78
6y - 4y = 144 - 78
2y = 66
y = 66/2 = 33
x = 4y/3 = (4 × 33)/3
x = 44
The total number of beads that they collected is
44 + 33 = 77 beads
