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Sagot :
Answer:
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
Step-by-step explanation:
Syrup A : 2 parts sugar , 8 parts of water .
Total = 10 parts
Syrup B : 3 parts sugar , 5 parts of water .
Total = 8 parts .
Mixture required 280 quarts , 3 parts sugar , 7 parts water
In 280 quarts , sugar = 280 x 3 / ( 3 + 7 )
sugar = 84 parts
Let volume of syrup A be x , volume of syrup B = 280 - x
sugar A = 2 x / 10 = 0.2 x
sugar B = 3 ( 280 - x ) / 8 = .375 ( 280 - x )
Total sugar = .2 x + .375 ( 280 - x ) = 84 .
.2 x + 105 - .375 x = 84
105 - 84 = .375 x - .2 x = .175 x
.175 x = 21
x = 21 / .175 = 120
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
Given that,
John has two different sugar syrups.
Syrup A is 2 parts of sugar and 8 parts of water, and Syrup B is 3 parts of sugar and 5 parts of water.
We have to determine,
How much of each should john mix together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
According to the question,
Syrup A: 2 parts sugar, 8 parts of water.
Total number of parts = 10 parts
Syrup B : 3 parts sugar, 5 parts of water.
The total number of parts = 8 parts.
The mixture required 280 quarts, 3 parts sugar, 7 parts water,
In 280 quarts, parts of sugar are,
[tex]= \dfrac{280 \times 3 }{ ( 3 + 7 )}\\\\= \dfrac{280 \times 3}{10}\\\\= 84[/tex]
Let the volume of syrup A be x,
And the volume of syrup B be 280 - x
[tex]Sugar\ A = \dfrac{2x}{10} \\\\Sugar \ A = 0.2 x[/tex]
[tex]Sugar \ B = \dfrac{3 ( 280 - x ) }{8 }\\\\Sugar \ B= .375 ( 280 - x )[/tex]
The total amount of sugar is,
[tex]0.2 x + 0.375 ( 280 - x ) = 84 \\\\0.2 x + 105 -0 .375 x = 84\\\\105 - 84 = 0.375 x - 0.2 x = 0.175 x\\\\ 0.175 x = 21\\\\x = \dfrac{21}{0.175}\\\\x = 120[/tex]
Therefore,
The volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts
Hence, John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
For more details, refer to the link.
https://brainly.com/question/11921451
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