Coming out of the grocery store, Ebree has eight coins, of which none is a half-dollar, that add up to $1.45. Unfortunately, on the way home she loses one of them. If the chances of losing a quarter, dime or nickel are equal, which coin is most probably lost?

Quarter?

Bart Simpson goes to the corner store and buys an equal number of 35 cent and 30 cent candies for $22.75 How many candies did he buy?
70?

1.

If dollars are included (as in Canada),
$1.45=1 dollar + 5 nickels + 2 dimes
If dollars are excluded,
$1.45=5 quarters + 2 nickels + 1 dime
Try to figure out the probability from these results.

1.
Let N=number of candies of each kind.
N=22.75/(0.35+0.30)=35
So how many candies did Bart buy?

So is my answers wrong?

Your answer is right.

I hope you worked out the problem by yourself, in which case you would have followed the same logic where 35 is the number of candies of EACH kind.

Ok Thanks! I showed my work but I wanted to make sure I did it correct:)

You're welcome!

To find out which coin is most probably lost, we need to calculate the possible combinations of eight coins that add up to $1.45. Then, we need to determine which combination is not possible with the given coins, assuming that none of them is a half-dollar.

Let's break down the possible coin combinations:

1. Using a quarter: Since we don't have any half-dollars, we can have either 5 quarters or 3 quarters with 5 dimes. However, using 3 quarters is not possible because the remaining 5 coins would have to add up to $1.45 - $0.75 = $0.70, which is not possible with the remaining dimes and nickels. Therefore, we have 1 possible combination with a quarter.

2. Using dimes and nickels: If we don't use any quarters, we have to use only dimes and nickels. We can calculate the possible combinations by trying all the values for dimes starting from 1 and calculating the corresponding combinations of nickels. However, to simplify the process, we can use the fact that the sum of 8 nickels is $0.40, which is less than the required $0.70. Therefore, we need to subtract 8 nickels from the total combination count.

Combining the possibilities from both cases, the total number of possible combinations is:

1 (quarter) + (number of combinations using only dimes and nickels) - 8 (nickels)

The number of combinations using only dimes and nickels can be determined using a combination formula. Given that we have 5 available spots for dimes and nickels (since we already used 3 spots for the quarters), we have to choose a combination of 5 from the total of 5 coins (dimes and nickels):

Combination(5, 5) = 1.

Substituting the values into the equation, we have:

1 (quarter) + 1 (combination of dimes and nickels) - 8 (nickels) = -6.

Since a negative value is not possible, it means that there are no combinations using only dimes and nickels that add up to $0.70. Therefore, the most probable lost coin is a quarter.

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To determine the number of candies Bart bought, we can set up an equation based on the given information.

Let's say Bart bought x candies of each type. The cost of the 35 cent candies would then be 35x, and the cost of the 30 cent candies would be 30x. The total cost of the candies is given as $22.75, so we have the equation:

35x + 30x = 2275.

Combining like terms, we get:

65x = 2275.

Dividing both sides by 65, we find:

x = 2275 / 65 = 35.

Therefore, Bart bought 35 candies of each type, resulting in a total of 35 + 35 = 70 candies.