The number of coins that Lana and Brad had were in the ratio

5x-8/2x+8=3x/2x

4x^2-40x=0 => x^2-10x=0 => x(x-10)=0, so x=10

5*10/2*10=50/20 => after giving 8 = > 42/28 and 42-28=14

D

Hi All,

Ratio questions such as these can certainly be solved with Algebra, and in many cases can be solved by TESTing THE ANSWERS. Here, since the numbers involved are relatively small, we can "brute force" the solution and focus on the basic Arithmetic involved:

We're told a number of Facts about the number of coins that Lana and Brad had:
1) To start, the ratio of coins was 5:2
2) After Lana gave Brad 8 coins, the ratio became 3:2

The question asks how many MORE coins Lana had than Brad AFTER she gave him the 8 coins.

From the initial ratio, we know that Lana had a multiple of 5 coins and Brad had an equivalent multiple of 2 coins. Since Lana gave Brad 8 coins, she clearly had to START with MORE than 8 coins. The smallest multiple of 5 that "fits" is 10, so we'll start there:

IF....
Lana = 10 coins; Brad = 4 coins
After 8 coins are given....
Lana = 2 coins; Brad = 12 coins
This does NOT match the 3:2 ratio. Lana needs to start off with LOTS more coins....

IF....
Lana = 30 coins; Brad = 12 coins
After 8 coins are given....
Lana = 22 coins; Brad = 20 coins
This does NOT match the 3:2 ratio

IF....
Lana = 40 coins; Brad = 16 coins
After 8 coins are given....
Lana = 32 coins; Brad = 24 coins
This does NOT match the 3:2 ratio, but it's getting close....

IF....
Lana = 50 coins; Brad = 20 coins
After 8 coins are given....
Lana = 42 coins; Brad = 28 coins
This MATCHES the 3:2 ratio

After the 8 coins are given, Lana has 42-28 = 14 more coins than Brad.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

another method to solve this

initially l/b =5/2 ..................l gives b 8 coins


now ratio is

l-8/b+8 = 3/2

question asks
( l has how many more coins than b now

now l has ( l-8) b has ( b+8) ...so l has how much more ) l-8 - ( b+8) = l-b -16 ,,,,,,

l - b = 5x - 2x = 3x .......


so l-b -16 = 3x -16

x has to be atleast 6 to get a positive no

3(6) - 16 = 2 not matching

3( 7) -16 = 5 not matching

........ 3(10) - 16 = 14 ( matches ) ...this is our answer ....

thank you

Let Lana initially have L coins and Brad initially have B coins.

As given: L = 5x and B = 2x
Finally, L' = 5x - 8 and B' = 2x + 8

To find: L' - B' = (5x - 8) - (2x + 8) = 3x - 16

Given: \(\frac{(5x-8)}{(2x+8)} = \frac{3}{2}\)

Upon solving this equation, we get: x = 10

This gives L' - B' = 3*10 - 16 = 14

Here's a variation of the above question for further practice:

The number of coins that Lana and Brad had were in the ratio of 5 : 2, respectively. After Lana gave Brad 8 of her coins, which of the following can be the difference of coins between Lana and Brad?

I . 8
II. 22
III. 26

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II and III


Best Regards

Japinder

The number of coins that Lana and Brad had were in the ratio of 5 : 2, respectively. After Lana gave Brad 8 of her coins, the ratio of the number of coins Lana had to the number Brad had was 3 : 2. As a result of this gift, Lana had how many more coins than Brad?

(A) 30
(B) 28
(C) 22
(D) 14
(E) 8

We have to determine the difference between the number of coins Lana has after she's given the eight coins and the number of coins Brad has after he's received the eight coins, in other words, (L-8) - (B+8) =?

We're given that L/B = 5/2 and that (L-8)/(B+8) = 3/2.
We should use these two equations to solve for L and B.

Begin by cross multiplying the second equation to give 2(L-8) = 3(B+8)
2L-16 = 3B +24
2L = 3B + 40

If L/B = 5/2, then multiplying both sides of the equation by B gives L= 5B/2.
Now substitute this into the previous equation:
2 (5B/2) = 3B + 40 => 5B = 3B +40 => 5B - 3B = 40 => 2B=40
B=20

Again since L/B=5/2, then L/20=5/2 => L=50

(L-8) - (B+8) = (50-8) - (20+8) = 42-28 = 14

We can let the initial ratio of Lana to Brad = 5x : 2x and create the equation:

(5x - 8)/(2x + 8) = 3/2

2(5x - 8) = 3(2x + 8)

10x - 16 = 6x + 24

4x = 40

x = 10

Therefore, as a result of the gift, Lana now has 5(10) - 8 = 42 coins and Brad has 2(10) + 8 = 28 coins. So Lana has 42 - 28 = 14 more coins than Brad.

Answer: D

5x-8/2x+8=3/2

10x-16=6x+24

4x=40 => x=10

5(10)-8 =42
2(10)+8=28

42-28 = 14

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