In a group of quarters and nickels, there are four more nickels than quarters. How many nickels and quarters are the if the coins are worth $2.30?
Plsmshow the solution, thanks
add up the values of the coins:
n = q+4, so
5(q+4) + 25q = 230
30q+20 = 230
30q = 210
q = 7
so, n=q+4 = 11
Sure! Let's solve this problem step by step.
Let's start by assigning variables to the number of quarters and nickels. Let q represent the number of quarters and n represent the number of nickels.
The problem tells us that there are four more nickels than quarters. So we have the equation: n = q + 4.
Now let's consider the value of the coins. The value of one quarter is $0.25, and the value of one nickel is $0.05. The total value of all the quarters can be calculated as 0.25*q, and the total value of all the nickels can be calculated as 0.05*n.
The problem tells us that the coins are worth $2.30 in total. So we can write the equation: 0.25*q + 0.05*n = 2.30.
Now we have a system of two equations:
n = q + 4
0.25*q + 0.05*n = 2.30.
We can solve this system of equations using substitution or elimination method.
Let's solve this system using the substitution method. Start by substituting the value of n from the first equation into the second equation:
0.25*q + 0.05*(q + 4) = 2.30.
Now let's simplify and solve for q:
0.25*q + 0.05q + 0.20 = 2.30.
0.30*q = 2.30 - 0.20.
0.30*q = 2.10.
Divide both sides of the equation by 0.30:
q = 2.10 / 0.30.
q = 7.
Now we know there are 7 quarters.
To find the number of nickels, substitute the value of q into the first equation:
n = 7 + 4.
n = 11.
So there are 7 quarters and 11 nickels in the group.
To check if this answer is correct, let's calculate the total value of the coins:
Total value = (0.25*q) + (0.05*n)
Total value = (0.25*7) + (0.05*11)
Total value = 1.75 + 0.55 = 2.30.
Since the total value matches the given value of $2.30, our solution is correct.