Bobby has only pennies, dimes, and quarters. One half of Bobby's coins are pennies. One fourth of his coins are quarters. Three of his coins are dimes. How many coins does Bobby have?
please help me figure this one out?
Bobby has 12 coins.
he has 3 dimes, 6 pennies, and 3 quarters
How did you get your answer? Please explain it to me?
i used the equation: 1/2x+1/4x+3=x
then add 1/2x and 1/4x: 3/4x+3=x
then subtract 3/4x on both sides:3=1/4x
then divide by 1/4x: 12=x
-12 coins is the answer :)
1/2 + 1/4 = 3/4
so 3/4 of his coins must be made up of pennies and quarters.
so that means the remaining 1/4 must be dimes
But we know that he has 3 dimes
think this way: 1/4 of what number is 3 ?
or
3 divided by 1/4 is .... ?
To solve this problem, we need to break it down into smaller parts. Let's start by assigning variables to the unknown quantities. Let's say that Bobby has a total of N coins.
According to the problem, one half of Bobby's coins are pennies. This means that N/2 coins are pennies.
Also, the problem states that one fourth of his coins are quarters, so N/4 coins are quarters.
Lastly, the problem mentions that three of his coins are dimes. So we know that Bobby has 3 dimes.
To find the total number of coins Bobby has, we can add up the number of each type of coin:
N = Number of pennies (N/2) + Number of quarters (N/4) + Number of dimes (3)
We need to solve for N.
To eliminate the fractions in the equation, we can multiply through by the lowest common multiple of the denominators, which is 4 in this case.
4N = (4/2)N + (4/4)N + 12
Simplifying the equation, we get:
4N = 2N + N + 12
Combining like terms, we have:
4N = 3N + 12
Subtracting 3N from both sides:
4N - 3N = 12
N = 12
Therefore, Bobby has a total of 12 coins.