Answer:
AJ picks 252 pounds
Step-by-step explanation:
Lets define the following letters for each name:
A is AJ
B is Blaze
L is Laurence
J is Jack
Now we will analyze the phrases one by one:
Blaze picks three times as many as Laurence means:
[tex]B = 3 * L[/tex]
Jack picks twice as many as Blaze.
[tex]J = 2 * B[/tex], ans using the previous one lets substitute B with 3 * L
[tex]J = 2 * B = 2 * (3 * L)[/tex]
[tex]J = 6 * L[/tex]
Aj picks three times as many as Laurence.
[tex]A = 3 * L[/tex]
The total weight of the oranges is 1092 pounds.
[tex]A + B + J + L = 1092[/tex]
We replace A, B & J in the last equation, with the previous results:
[tex]A + B + J + L = 1092[/tex]
[tex](3*L) + (3*L) + (6*L) + L = 1092[/tex], grouping using L as common factor:
[tex](3+3+6+1) * L = 1092[/tex]
[tex]13 * L = 1092[/tex], then isolating L:
[tex]L = 1092 / 13[/tex]
[tex]L = 84[/tex] pounds (for Laurence)
Finally replacing L in the previous equations:
[tex]A = 3 * L = 3 * 84 = 252[/tex] pounds (for Aj)
[tex]B = 3 * L = 3 * 84 = 252[/tex] pounds (for Blaze)
[tex]J = 6 * L = 6 * 84 = 504[/tex] pounds (for Jack)
