Question

A boy had half as many 5 cent coins as he had 1 cent coins. If he changed all the 1 cent coins to 2 cent coins at the bank, he would have: A. 2/5 as many coins B. 2/3 as many coins, C. 5/6 as many or C, 5/8 as many. I do know that it is 2/3 more, I just want an in depth explanation. Thanks!

Answer 1

Where y represents the total number of coins and 0.5x represents the number of 5 cent coins and x represents the number of 1 cent coins...
y = 0.5x + x
= 1.5x

1/2x + 2x = 2.5x
If he exchanged 1 cent coins for 2 cent coins, he would have half the same number of 2 cent coins as he had for 5 cent coins. Instead of 2x, you would have "x" and...
y = 0.5x + 0.5x = x
y = 1x

Divide slopes..
1 / 1.5 = 2/3 or 0.67.

The answer is 2/3 so Choice B is the answer.