Problem Solving

Hello,

Can you please tell my if my solution is correct here:

Pedro has some coins in his pocket, some are 5-cent coins and some are 25-cent coins. If the average value of each coin in Pedro's pocket is 10 cents and he has $8 in his pocket, what is the total value of his 5-cent coins?


A) $1
B) $2
C) $3
D) $4
E) $6

OA Given: E

This is from "GMAT Word Problems" book.


f --------------f+tf-------------------tf
5---------------10---------------------25

f/tf = (25-10)/(10-5) = 3/1

Since the total is $8

3x + x = 800
=> 4x = 800
=> x = 200

Tot. value of five cent coins = 3x = 3(200) = 600 cents = $6/-


I was wondering if this is correct?


Thanks a lot,
Sri

gmattesttaker2 wrote:Hello,

Can you please tell my if my solution is correct here:

Pedro has some coins in his pocket, some are 5-cent coins and some are 25-cent coins. If the average value of each coin in Pedro's pocket is 10 cents and he has $8 in his pocket, what is the total value of his 5-cent coins?


A) $1
B) $2
C) $3
D) $4
E) $6

This is a MIXTURE problem.
A certain number of 5-cent coins are combined with a certain number of 25-cent coins to form a MIXTURE with an average value of 10 cents per coin.
To solve, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 coin values on a number line, with the values for the two types of coins on the ends and the value for the mixture in the middle.
5-----------10-----------25

Step 2: Calculate the distances between the values.
5-----5-----10-----15-----25

Step 3: Determine the ratio in the mixture.
The required ratio of 5-cent coins to 25-cent coins is equal to the RECIPROCAL of the distances in red.
(5-cent coins) : (25-cent coins) = 15:5 = 3:1.

Implication:
Of every 4 coins, 3 are 5-cent coins and 1 is a 25-cent coin.
Thus:
Total value of every 4 coins = (3*5) + (1*25) = 40 cents.
Since (total value of 3 5-cent coins)/(total value of every 4 coins) = 15/40 = 3/8, the 5-cent coins must account for 3/8 of Pedro's $8:
(3/8) * 8 = 3.

The correct answer is C.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html