Mary has a $5 and some nickels. Jerry has $2 and
some dimes. Mary has the same of nickels as Jerry has dimes. How many coins do they each have if they have the same total amount?
Let's assume Mary has $5 and Jerry has $2. To make the total amount the same, Mary must have the same amount of nickels as Jerry has dimes.
Let's assume the value of each nickel is $0.05 and the value of each dime is $0.10.
Let's say Mary has x nickels and Jerry has x dimes.
The value of x nickels is $0.05 * x = $0.05x.
The value of x dimes is $0.10 * x = $0.10x.
The total amount Mary has is $5 + $0.05x, and the total amount Jerry has is $2 + $0.10x.
Since they have the same total amount, we can set up the equation:
$5 + $0.05x = $2 + $0.10x.
Simplifying the equation, we get:
$5 - $2 = $0.10x - $0.05x,
$3 = $0.05x.
Dividing both sides of the equation by $0.05, we get:
x = $3 / $0.05,
x = 60.
Mary and Jerry each have 60 coins. Mary has 60 nickels and Jerry has 60 dimes.
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Let's solve this step-by-step.
1. Let's assign variables to the given information:
- Let "x" represent the number of nickels Mary has.
- Let "y" represent the number of dimes Jerry has.
2. Mary has $5 and some nickels, so the total amount Mary has in cents is (5 * 100 + x * 5) cents.
3. Jerry has $2 and some dimes, so the total amount Jerry has in cents is (2 * 100 + y * 10) cents.
4. Mary has the same amount as Jerry, so we can equate their total amounts in cents:
5 * 100 + x * 5 = 2 * 100 + y * 10
5. Simplifying the equation:
500 + 5x = 200 + 10y
6. Rearranging the equation:
5x = 10y - 300
7. Dividing both sides by 5:
x = 2y - 60
8. We also know that Mary has the same number of nickels as Jerry has dimes, so x = y.
9. Substituting x = y into equation (8):
y = 2y - 60
10. Simplifying the equation:
-y = -60
11. Multiplying both sides by -1:
y = 60
12. Substituting y = 60 back into equation (8):
x = 2 * 60 - 60
x = 120 - 60
x = 60
13. Mary has 60 nickels and Jerry has 60 dimes.
Therefore, Mary has 60 nickels and Jerry has 60 dimes.
To find the number of coins each person has, we need to set up the following equations:
Let's assume Mary has x nickels.
Since Jerry has the same number of nickels as Mary has dimes, Jerry also has x dimes.
The value of x nickels is 5 * x = 5x cents.
The value of x dimes is 10 * x = 10x cents.
The total amount Mary has is 5x cents.
The total amount Jerry has is 2 + 10x cents.
Since they have the same total amount, we can set up the equation:
5x = 2 + 10x
Let's solve this equation for x:
5x - 10x = 2
-5x = 2
x = -2/5
However, since we can't have a negative number of coins, this solution doesn't make sense in this context.
Therefore, there is no solution to this problem, and it is not possible for Mary and Jerry to have the same total amount with the given information.