SOLUTION: 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 h

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 b)how many cards did Miya win from jack altogether
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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
=
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
=
Replace .9j with 3.3m
=
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
= 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 =
x = 102 cards
Total cards won by Miya; 22 + 102 = 124 cards

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