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Given
A tea that is 22% jasmine is blended with a tea that is 13% jasmine
Find out the how many pounds of the 22% jasmine tea are used to make 10lb of tea that is 19.3% jasmine.
To proof
Let us assume that the a tea that is 22% jasmine is blended = a
Let us assume that the a tea that is 13% jasmine is blended = b
Total amount of tea made = 10lb
the equation be
a + b = 10
as given
jasmine tea are used to make 10lb of tea that is 19.3% jasmine.
write 22% in the decimal form
= 0.22
write 13% in the decimal form
= 0.13
write 19.3% in the decimal form
= 0.193
than the equation be
0.22a + 0.13b = 0.193 × 10
on simplify
22a + 13b = 193
two equation becomes
22a + 13b = 193 and a + b = 10
multiply a + b = 10 by 13 and subtracted from the 22a + 13b = 193
we get
22a - 13a + 13b -13b = 193 - 130
9a = 63
a = 7lb
put this value in the a + b = 10
we get
7 + b = 10
b = 3lb
Therefore the 22% jasmine tea are used to make 10lb of tea that is 19.3% jasmine is 7 lb .
Hence proved