Question 1095929: One winter Khalid and ashraf earned rs. 77.50 a month from their business.when summer came, Khalid lost one-fifteenth of his customers, ashraf lost one-tenth of his, and then total monthly earnings were then rs. 71.how much did each boy earn per month in the winter?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let K equal the amount that khalid makes.
let A equal the amount that ashraf makes.
in the winter, you get:
K + A = 77.5
in the summer khalid lost 1/15 of his customers and ashraf lost 1/10 of his.
if you assume that each made the same amount of money from each of their customers, then khalid lost 1/15th of his revenue and ashraf lost 1/10 of his revenue.
this means that khalid made 14/15 of his winter revenue in the summer and ashraf made 9/10 of his winter revenue in the summer.
you get:
14/15 * K + 9/10 * A = 71
you have two equations that needs to be solved simultaneously.
they are:
K + A = 77.5
14/15 * K + 9/10 * A = 71
multiply both sides of the second equation by (15 * 10) to remove the fractions.
you get:
first equation is K + A = 77.5
second equation is 140 * K + 135 * A = 10650
140 * K is the result of (14 * K / 15) * 10 * 15 which results in 14 * K * 10 which results in 140 * K.
135 * A is the result of (9 * A / 10) * 10 * 15 which results in 9 * A * 15 which results in 135 * A.
10650 is the result of 71 * 10 * 15 which results in 10650
your two equations that need to be solved simultaneously are now:
K + A = 77.5
140K + 135A = 10650
multiply both sides of the first equation by 140 and leave the second equation as is to get:
140K + 140A = 10850
140K + 135A = 10650
subtract the second equation from the first to get:
5A = 200
solve for A to get A = 200 / 5 = 40
since K + A = 77.5, then K must be equal to 37.5 because 40 + 37.5 = 77.5
you have K = 37.5 and A = 40
K + A = 37.5 + 40 = 77.5
14/15 * K + 9/10 * A = 14/15 * 37.5 + 9/10 * 40 which is equal to 35 + 36 which is equal to 71.
everything checks out so the solution can be assumed to be good.
note that 14/15 * K is the same as K - 1/15 * K since K - 1/15 * K becomes 37.5 - 2.5 which becomes 35.
similarly, 9/10 * A is the same as A - 1/10 * A since A - 1/10 * A becomes 40 -
4 which becomes 36.
you were asked how much each boy made in the winter.
khalid made 37.5 and ashraf made 40 in the winter.
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