ardz24 wrote:What is the ratio of nickels to dimes in a bag of change that contains only nickels and dimes? (nickel = $0.05; dime = $0.1)

(1) The total amount of money in the bag is $8.70.
(2) If the number of nickels was increased by 10%, the number of nickels in the bag would be 50% of the total number of dimes in the bag.

Statement 1:
Since each nickel is worth 5 cents, each dime is worth 10 cents, and the total amount is 870 cents, we get:
5n + 10d = 870.
If n=2 and d=86, then n/d = 2/86 = 1/43.
If n=4 and d=85, then n/d = 4/85.
Since n/d can be different values, INSUFFICIENT.

Statement 2;
Case 1: n=10
Here, n increased by 10% = 10 + (10% of 10) = 10 + 1 = 11.
Since the value in blue must be half the value of d, d=22.
In this case, n/d = 10/22 = 5/11.

Case 2: n=20
Here, n increased by 10% = 20 + (10% of 20) = 20 + 2 = 22.
Since the value in blue must be half the value of d, d=44.
In this case, n/d = 20/44 = 5/11.

In each case, the value of n/d is THE SAME.
SUFFICIENT.

The correct answer is B.

Statement 2, approached algebraically:
n increased by 10% = 110% of n = (110/100)n = (11/10)n.
Since the value in blue is equal to 1/2 of d, we get:
(11/10)n = (1/2)d
n/d = (1/2)(10/11) = 5/11.
SUFFICIENT.