Question

A tea that is 22% jasmine is blended with a tea that is 13% jasmine. How many pounds of the 22% jasmine tea are used to make 10lb of tea that is 19.3% jasmine

Answer 1

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

$= \frac{22}{100}$

= 0.22

write 13%  in the decimal form

$=\frac{13}{100}$

= 0.13

write 19.3%  in the decimal form

$=\frac{19.3}{100}$

= 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