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## A farmer shared 469 tomatoes among three workers, Peter, Gem and Tom. Gem received 16 more than Peter. Tom received 3 times as many as peter.

A farmer shared 469 tomatoes among three workers, Peter, Gem and Tom. Gem received 16 more than Peter. Tom received 3 times as many as peter. Calculate the numbers of tomatoes Peter received.
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# 1 Answer

Hi again Shelcia;
I love these questions!  They are so much fun!
P=P
G=P+16
T=3P

469=P+G+T
Let's substitute as we want to begin with one variable, not three...
469=P+(P+16)+(3P)
469=P+P+16+3P
Let's combine like terms...
469=5P+16
Let' subtract 16 from both sides...
469-16=5P+16-16
453=5P
At this point, I would like to divide both sides by 5.  However, 453 cannot be evenly divided by this number. The farmer did not give anyone a partial tomato.  I must assume that there is a typographical error.  Perhaps this is 450+16=466?
450=5P
(450)/5=(5P)/5
90=P

G=P+16
G=90+16=106

T=3(P)
T=3(90)=270

Let's check our work...
466=90+106+270
466=466

Please let me know if there is a typographical error.  I can only speculate on what happened.
Your instructor had the word problem recorded in his/her notes, then reproduced it on the marker-board.  You recorded it in your notes and then reproduced it herein.  It is a long way to go, and did not quite make it.

# Comments

Dear Vivian,                                                                                                                                                 Thank you for your help. But i
I cannot quite understand the answer . Is there a simpler way for you to explain this to me?
Yours truly'
Shelcia

Hi Shelcia;
I need you to proofread the original question.  The mathematics do not work.  Working with your numbers would require the specification that one individual received a partial tomato.  Otherwise, I am not certain I understand what you do not understand.
TOTAL=GEM+TOM+PETER
TOTAL=(PETER+16)+[3(PETER)]+PETER