Sam and Sue have only nickels and dimes. Sue has 35¢. Sam has the same number of dimes as Sue has nickels, and he has half as many nickels as Sue has dimes. How many nickels does Sue have?
If Sue has d dimes and n nickels, then
10d + 5n = 35
d=1 and n=5
or d=2 and n=3
or d=3 and n=1
Since Sam has d/2 nickels, d must be even.
So Sue has 3 nickels
please help me with this question
To find out how many nickels Sue has, we need to analyze the given information.
Let's start by understanding the relationship between nickels and dimes for Sam and Sue. We know that Sam has the same number of dimes as Sue has nickels. Therefore, the number of dimes Sam has is equal to the number of nickels Sue has.
Next, we are told that Sam has half as many nickels as Sue has dimes. This means that the number of nickels Sam has is half the number of dimes Sue has.
Now, let's calculate the number of dimes Sam has.
Since Sue has 35¢ and only nickels and dimes, we can express that in terms of nickels and dimes:
35¢ = 5d + 10n, where d represents the number of dimes and n represents the number of nickels.
Since Sam has the same number of dimes as Sue has nickels, we can substitute n with d in the equation:
35¢ = 5d + 10d
Simplifying the equation, we have:
35¢ = 15d
To find the value of d (the number of dimes), divide both sides of the equation by 15:
35¢ / 15 = d
2.33 = d
Since we can't have a fraction of a dime, we round down to the nearest whole number:
d ≈ 2
Now that we know Sam has 2 dimes, let's calculate the number of nickels Sue has.
Since Sam has half as many nickels as Sue has dimes, we multiply the number of dimes by 0.5 to get the number of nickels:
2 dimes * 0.5 = 1 nickel
Therefore, Sue has 1 nickel.