Question 1081008
 Jack and Miya had some cards.
In a game, Jack lost 1/10 of his card to Miya.
 After Jack lost his cards to Miya,the ratio of the number of cards jack had to the number of cards Miya had was 3:1.
The next day, after jack lost more cards to Miya, the ratio became 4:7 and Miya had 72 more cards than jack.
a) what was the ratio of the number of cards jack had to the number of cards Miya had at first
:
let j = no. of cards J had originally
let m = no. of cards M had
" Jack lost 1/10 of his card to Miya. After Jack lost his cards to Miya, the ratio of the number of cards jack had to the number of cards Miya had was 3:1."
therefore
{{{(.9j)/(1.1m)}}} = {{{3/1}}}
cross multiply
1(.9j) = 3(1.1m)
.9j = 3.3m
"jack lost more cards to Miya, the ratio became 4:7"
let x = no. of more lost to Miya
{{{(.9j-x)/(1.1m+x)}}} = {{{4/7}}}
Replace .9j with 3.3m
{{{(3.3m-x)/(1.1m+x)}}} = {{{4/7}}}
cross multiply
7(3.3m-x) = 4(1.1m+x)
23.1m - 7x = 4.4m + 4x
23.1m - 4.4m = 4x + 7x
18.7m = 11x
" and Miya had 72 more cards than jack.
(1.1m + x) - (.9j-x) = 72
1.1m - .9j + x + x = 72
1.1m - .9j + 2x = 72
replace .9j with 3.3m, replace x with .9m
1.1m - 3.3m + 2(.9m) = 72
1.1m - 3.3m + 1.8m = 72
-2.2m + 2x = 72
2x = 2.2m + 72
divide by 2
x = 1.1m + 36
Using the equation 18.7m = 11x, replace x with 1.1m+36
18.7m = 11(1.1m + 36)
18.7m = 12.1m + 396
18.7m - 12.1m = 396
6.6m = 396
m = 396/6.6
m = 60 cards Miya originally
then
.9j = 3.3(60)
j = 198/.9
j = 220 cards Jack originally
:
a) what was the ratio of the number of cards jack had to the number of cards Miya had at first
{{{220/60}}} = 11:3
:
 b)how many cards did Miya win from jack altogether 
First time: .1(220) = 22 cards
2nd time: find x,we know:
11x = 18.7m
11x = 18.7(60)
x = {{{1122/11}}}
x = 102 cards
Total cards won by Miya; 22 + 102 = 124 cards