SOMEONE PLEASE ANSWER THIS FOR MY FIFTH GRADE COUSIN...IM NOT SMARTER THAN A FIFTH GRADER CLEARLY

AJ, Blaze, Laurence, and Jack pick oranges. Blaze picks three times as many as Laurence. Jack picks twice as many as Blaze. Aj picks three times as many as Laurence. The total weight of the oranges is 1092 pounds. How many pounds does AJ pick?

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ngallia ngallia · Answer 1 · 2019-10-23T20:38:16+02:00

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)