The royal fruit company producers two of fruit drinks. The first type is 55% pure fruit juice and the second type is 80 % pure fruit juice. The company is attempting to produce a fruit that contains 75% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 160 pints of a mixture that is 75% pure fruit water?
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A. The first type is 55% pure fruit juice and
B. The second type is 80 % pure fruit juice.
C. The third type is 75 %.
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The total pints of C is the result of the mixture of pints of A and B
C= A+B ( i )
The expression that relates the proportion of water and fruit in pints
0.75 C = 0.55 A + 0.8 B (ii)
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C= A+B
160 = A+ B
A= 160 -B
Replacing in (ii)
0.75* 160 = 0.55 (160-B) + 0.8 B
120= 88 - 0.55 B + 0.8 B
B (0.8-0.55) = 120 -88
B= 32/ 0.25
B= 128
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A= 160 -B
A= 160 -128
A= 32
Could you confirm for me if you see the updates?
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Verifying
0.75 * 160 = 0.55 A + 0.8 B
120 = 0.55 * 32 + 0.8* 128
120= 17.6 + 102.4
120= 120
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To produce 160 pints of a mixture that is 75% pure fruit water, we need
32 pints of the first type pint (55% pure fruit juice) and 128 pints of the second type pint (80 % pure fruit juice).
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