# University math word problem?

Together, Al, Barb, Cal, Di and Ed earned a total of \$150 for the Math Club fundraiser, but in unequal amounts. To be fair, they decide to split up the money equally. In order to do this, first Barb gave half her earnings to Al. Next, Cal gave 1/3 of his earnings to Barb. Then Di gave 1/4 of her earnings to Cal. Finally, Ed gave 1/6 of his earnings to Di. How much money did Al originally earn? (Remember: Your answer must show appropriate work or reasoning.) Relevance

Let A, B, C, D, E be the amounts that Al, Barb, Cal, Di and Ed started with.

In order to have \$150 divided into 5 equal shares, everyone must end up with \$30.

Let's work backwards.

Ed gave 1/6 of his earnings to Di.

He keeps (5/6)E which is \$30.

(5/6)E = 30

E = 30 * 6/5

E = 6 * 6

E = 36

The amount he gave away to Di (1/6) was \$6.

Di gave 1/4 of her earnings to Cal.

She keeps (3/4)D and with the \$6 from Ed would have \$30.

(3/4)D + 6 = 30

(3/4)D = 24

D = 24 * 4/3

D = 8 * 4

D = 32

The amount she gave away to Cal (1/4) was \$8.

Cal gave 1/3 of his earnings to Barb.

He keeps (2/3)C and with the \$8 from Di would have \$30.

(2/3)C + 8 = 30

(2/3)C = 22

C = 22 * 3/2

C = 11 * 3

C = 33

The amount she gave away to Barb (1/3) was \$11.

Barb gave 1/2 of her earnings to Al.

She keeps (1/2)B and with the \$11 from Cal would have \$30.

(1/2)B + 11 = 30

(1/2)B = 19

B = 19 * 2/1

B = 38

The amount she gave away to All was \$19.

In order to end up with \$30, Al must have had \$11.

A = 11

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• After all the giving of earnings, everybody had \$30 each. (\$150 / 5)

Ed must have originally earned \$36, in order to have \$30 after giving 1/6 of \$36 to Di.

After receiving the \$6 from Ed, Di would have \$30.  So Di had \$24 after giving 1/4 of her original earnings to Cal.  So she must have earned \$32 originally, and gave \$8 to Cal.

After receiving the \$8 from Di, Cal would have \$30. So Cal had \$22 after giving 1/3 of his original earnings to Barb.  So he must have earned \$33 originally, and gave \$11 to Barb.

After receiving the \$11 from Cal, Barb would have \$30.  So Barb had \$19 after giving 1/2 of her original earnings to Al.  So she must have earned \$38 originally, and gave \$19 to Al.

After receiving \$19 from Barb, Al would have \$30.  So Al must have earned \$11 originally.

[Although I'm not seeing how the Math Club got anything.]

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