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The number of 20-cent coins in a basket was 100% more than the number of 10-cent coins. 13 twenty-cent coins were taken out and exchanged for 10-cent coins. The number of 20-cent coins became 5/8 less than the number of 10-cent coins. How much money is there in the basket?

 Mar 19, 2023
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Let's start by assigning variables to represent the unknown quantities in the problem:

Let x be the number of 10-cent coins in the basket.


Then, the number of 20-cent coins in the basket is 2x, since it's given that there are 100% more 20-cent coins than 10-cent coins.


After 13 twenty-cent coins are exchanged for 10-cent coins, there are 2x-13 twenty-cent coins left in the basket, and the number of 10-cent coins in the basket is x+13*(2/1) = x+26.
According to the problem, after the exchange, the number of 20-cent coins left in the basket is 5/8 less than the number of 10-cent coins. Using this information, we can write the following equation:

 

2x - 13 = (3/8)*(x + 26)

Multiplying both sides by 8 to eliminate the fraction, we get:

16x - 104 = 3x + 78

Solving for x, we get:

13x = 182

x = 14 - Number of original 10-cent coins

 

Then, the number of 20-cent coins in the basket before the exchange was 2x = 28.

 

The total value of the coins in the basket before the exchange was (14 x 10) + (28 x 20) = 700 cents or $7.00

Therefore, there is $7.00 worth of coins in the basket.

 Mar 19, 2023

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