SOLUTION: While Mrs. Teacher was in China she decided to buy gifts for her wonderful students. Bracelets cost 12 Chinese dollars and necklaces cost 10 chinese dollars. Mrs. Teacher bought

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Question 163538: While Mrs. Teacher was in China she decided to buy gifts for her wonderful students. Bracelets cost 12 Chinese dollars and necklaces cost 10 chinese dollars. Mrs. Teacher bought a total of 55 bracelets and necklaces and spent a total of 620 Chinese dollars. How many bracelts and necklaces did the teacher buy. Show all work and explain your answer.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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While Mrs. Teacher was in China she decided to buy gifts for her wonderful students. Bracelets cost 12 Chinese dollars and necklaces cost 10 Chinese dollars. Mrs. Teacher bought a total of 55 bracelets and necklaces and spent a total of 620 Chinese dollars. How many bracelets and necklaces did the teacher buy. Show all work and explain your answer.
:
Let b = no. of bracelets
Let n = no. of necklaces
:
total items equation
b + n = 55
:
Total cost equation
12b + 10n = 620
:
Arrange the 1st equation so we can use it for substitution:
b + n = 55
n = 55-b; subtracted b from both sides
:
Substitute (55-b) for n in the cost equation, find b
12b + 10(55-b) = 620
:
12b = 550 - 10b = 620; multiplied what's inside the brackets
:
12b - 10b = 620 - 550; subtracted 550 from both sides
:
2b = 70
:
b = 70%2F2; divided both sides by 2
b = 35 bracelets
:
Find n
n = 55 -b
n = 55 - 35
n = 20 necklaces
:
Check our solution in the cost equation
12b + 10n = 620
12(35) + 10(20) = 620
420 + 200 = 620; confirms our solutions