SOLUTION: Please help me solve this equation: Frank, Dawn and Robert went to the grocery store to purchase some sandwich meat. Frank bought 300 grams of ham and 200 grams of turkey breast

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Question 352472: Please help me solve this equation:
Frank, Dawn and Robert went to the grocery store to purchase some sandwich meat. Frank bought 300 grams of ham and 200 grams of turkey breast for $8.90. Dawn bought 100 grams of ham and 300 grams of chicken breast for $9.00. Robert bought 200 grams of turkey breast and 200 grams of chicken breast for $9.40. What are the prices / 100 grams for ham, turkey breast and chicken breast?
Thanks so much!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = price/100 grams ham
Let b = price/100 grams turkey breast
Let c = price/100 grams chicken breast
given:
(1) 3a+%2B+2b+=+890 (in cents)
(2) 1a+%2B+3c+=+900
(3) 2b+%2B+2c+=+940
---------------
There are 3 equations and 3 unknowns, so
it's solvable
Subtract (1) from (3)
(3) 2b+%2B+2c+=+940
(1) -3a+-+2b+=+-890
2c+-+3a+=+50
2c+=+3a+%2B+50
c+=+%281%2F2%29%2A%283a+%2B+50%29
Substitute this in (2)
a+%2B+%283%2F2%29%2A%283a+%2B+50%29+=+900
2a+%2B+9a+%2B+150+=+1800
11a+=+1650
a+=+150
Substitute this in (2)
(2) 1a+%2B+3c+=+900
150+%2B+3c+=+900
3c+=+750
c+=+250
Substitute in (3)
(3) 2b+%2B+2%2A250+=+940
2b+=+940+-+500
2b+=+440
b+=+220
$1.50 = price/100 grams ham
$2.20 = price/100 grams turkey breast
$2.50 = price/100 grams chicken breast