Question 1018938
1. Brass is an alloy made by melting and mixing copper and zinc. A metallurgist has two brass alloys, one that is 65% copper and one that is 90% copper. He would like to combine a portion of each alloy to produce 500 g of a new alloy that is 75% copper.
Quantity:: c + z = 500 grams
Copper::: 65c+90z = 75*500
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65c + 65z = 65*500
65c + 90z = 75*500
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Subtract and solve for "z"::
25z = 10*500
z = (2/5)500 = 200 grams (amt. of 90% alloy needed)
c = 500-200 = 300 grams (amt. of 65% alloy needed)
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3. For a local carnival, adult tickets cost $32 and child tickets cost $14. If 193 people attended the carnival, and they paid $4 034 altogether, how many adults and how many children were there? 
a. Write a system of equations that can be used to represent this scenario.
Quantity:: a + c = 193 people
Value::: 32a+14c = 4,034
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Modify::
14a + 14c = 14*193
32a + 14c = 4034
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18a = 1332
a = 74 (# of adult tickets)
c = 193-74 = 119 (# of child tickets)

b. Solve the system of equations.

c. How many adults and how many children were there?

d. Does the conclusion agree with the original information?

4. Tanya has 44 quarters and dimes worth $8.30. 
How many of each type of coin does she have?
q + d = 44 coins
25q+10d = 830
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25q + 25d = 25*44
25q + 10d = 830
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Subtract and solve for "d"::
15d = 270
d = 18 (# of dimes)
q = 44-18 = 26 (# of dimes)
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Cheers,
Stan H.
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Answer: