Answer:
The system of equation to determine the quantity of nickels and quarters is simultaneous equation.
Nickels = 17
Quarters = 22
Step-by-step explanation:
Given
Let n represent number of nickels
Let q represent number of quarters
From line 1 of the question, we understand that
Total coins = 39
So, n + q = 39 because the made up of the nickels and the quarters
It's also stated that the total value of these 39 coins is $6.35.
First, it should be noted that
1 nickel is worth 0.05 and 1 quarter is worth 0.25, we can represent the total value of the coins with the following equation
0.05n + 0.25q = 6.35
At this point, we have two equation such can be solved simultaneously
n + q = 39 ------- (1)
0.05n + 0.25q = 6.35 ------- (2)
So, the system of equation to determine the quantity of nickels and quarters is simultaneous equation.
Solving further.....
Make q the subject of formula in equation (1)
q = 39 - n
Substitute 39 - n for q in equation 2
0.05n + 0.25q = 6.35 becomes
0.05n + 0.25(39 - n) = 6.35
0.05n + 9.75 - 0.25n = 6.35
Collect like terms
0.05n - 0.25n = 6.35 - 9.75
-0.2n = -3.4
Divide through by -0.2
-0.2n/-0.2 = -3.4/-0.2
n = 17
Recall that q = 39 - n
Substituton 17 for n in this equation
q = 39 - 17
q = 22
Hence, there are 17 nickels and 22 coins
