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.

## 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.

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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.

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