Your uncle has 36 coins in nickels and quarters. The value of his nickels is 1/15 of the value of his quarters. Find the number of nickels. Please show progress in answer.
number of nickels ---- x
number of quarters --- 36-x
value of nickels = 5x
value of quarters = 25(36-x)
"The value of his nickels is 1/15 of the value of his quarters" ---> 5x = (1/15)(25)(36-x)
times 5
25x = 25(36-x)
75x = 900 - 25x
100x = 900
x = 9
so 9 nickels and 27 quarters
To solve this problem, let's start by assigning variables to the unknown quantities.
Let's call the number of nickels "n" and the number of quarters "q".
We are given that your uncle has a total of 36 coins, so we can write an equation:
n + q = 36 (equation 1)
We are also given that the value of the nickels is 1/15 of the value of the quarters. The value of a nickel is $0.05, and the value of a quarter is $0.25.
We can set up another equation based on this information:
0.05n = (1/15)(0.25q)
Simplifying this equation, we have:
0.05n = 0.0167q
To eliminate the decimals, we can multiply both sides of the equation by 100:
5n = 1.67q (equation 2)
Now we have a system of two equations with two variables:
n + q = 36 (equation 1)
5n = 1.67q (equation 2)
We can now use one of several methods to solve this system of equations, such as substitution or elimination. Let's use substitution:
From equation 1, we can isolate "q" by subtracting "n" from both sides:
q = 36 - n
Now we can substitute this expression for "q" into equation 2:
5n = 1.67(36 - n)
Distribute 1.67:
5n = 60.12 - 1.67n
Combine like terms:
6.67n = 60.12
Divide both sides by 6.67:
n = 9
Therefore, your uncle has 9 nickels.