Can this be solved?
Jenny has 11 coins in her pocket, all of which are either nickels or dimes. If the value of the coins is 754, how many of each type of coin does she have?
Yes, this problem can be solved. To find out how many of each type of coin Jenny has, we can set up a system of equations.
Let's say Jenny has x nickels and y dimes. Since Jenny has a total of 11 coins, we know that x + y = 11.
We also know that the value of the coins is 754 cents. Since each nickel is worth 5 cents and each dime is worth 10 cents, the value of the nickels will be 5x and the value of the dimes will be 10y. Thus, we can write a second equation:
5x + 10y = 754.
Now we have a system of two equations with two variables. To solve this system, we can use one of several methods, such as substitution or elimination. Let's solve it using the substitution method.
From the first equation, we can express x in terms of y as x = 11 - y. We can substitute this expression for x in the second equation:
5(11 - y) + 10y = 754.
Now, we can simplify and solve for y:
55 - 5y + 10y = 754,
5y = 754 - 55,
5y = 699,
y = 699/5 = 139.8.
Since we cannot have a fraction of a coin, we can deduce that y must be a whole number. Therefore, Jenny has 139 dimes.
Now, substitute this value of y back into the first equation to find x:
x + 139 = 11,
x = 11 - 139,
x = -128.
Since we cannot have a negative number of coins, we can deduce that x must also be a whole number. Therefore, Jenny has 0 nickels.
In conclusion, Jenny has 0 nickels and 139 dimes.